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Trigonometric Ratio and Identites

57 questions · Mathematics · JEE Main

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JEE Main
Mathematics
Trigonometric Ratio and Identites

Trigonometric Ratio and Identites

57 questions · Mathematics · JEE Main

If $10 sin^{4} θ + 15 cos^{4} θ = 6$ , then the value of $\frac{27 cosec ^{6} θ + 8 s e c ^{6} θ}{16 s e c ^{8} θ}$ is2025 · 4 Apr · Shift 1 · Q33 · MCQ
If for $θ \in [- \frac{π}{3}, 0]$ , the points $(x, y) = (3 tan (θ + \frac{π}{3}), 2 tan (θ + \frac{π}{6}))$ lie on $x y + α x + β y + γ = 0$ , then $α^{2} + β^{2} + γ^{2}$ …2025 · 7 Apr · Shift 1 · Q35 · MCQ
The value of $(sin 7 0^{\circ}) (cot 1 0^{\circ} cot 7 0^{\circ} - 1)$ is2025 · 23 Jan · Shift 1 · Q33 · MCQ
Let the range of the function $f (x) = 6 + 16 cos x \cdot cos (\frac{π}{3} - x) \cdot cos (\frac{π}{3} + x) \cdot sin 3 x \cdot cos 6 x, x \in R$ be $[α, β]$ . Then the distance of the point $(α, β)$ …2025 · 23 Jan · Shift 2 · Q34 · MCQ
If $r = 1 \sum 13 {\frac{1}{s i n ( \frac{π}{4} + ( r - 1 ) \frac{π}{6} ) s i n ( \frac{π}{4} + \frac{r π}{6} )}} = a 3 + b, a, b \in Z$ , then $a^{2} + b^{2}$ is equal to :2025 · 28 Jan · Shift 2 · Q40 · MCQ
If $sin x + sin^{2} x = 1$ , $x \in (0, \frac{π}{2})$ , then $(cos^{12} x + tan^{12} x) + 3 (cos^{10} x + tan^{10} x + cos^{8} x + tan^{8} x) + (cos^{6} x + tan^{6} x)$ is equal to:2025 · 29 Jan · Shift 2 · Q40 · MCQ
If $tan A = \frac{1}{x ( x ^{2} + x + 1 )}, tan B = \frac{x}{x ^{2} + x + 1}$ and $tan C = (x^{- 3} + x^{- 2} + x^{- 1})^{1/2}, 0 < A, B, C < \frac{π}{2}$ , then $A + B$ …2024 · 1 Feb · Shift 1 · Q34 · MCQ
Suppose $θ \in [0, \frac{π}{4}]$ is a solution of $4 cos θ - 3 sin θ = 1$ . Then $cos θ$ is equal to :2024 · 5 Apr · Shift 1 · Q47 · MCQ
If $sin x = - \frac{3}{5}$ , where $π < x < \frac{3 π}{2}$ , then $80 (tan^{2} x - cos x)$ is equal to2024 · 8 Apr · Shift 1 · Q46 · MCQ
If the value of $\frac{3 c o s 3 6 ^{\circ} + 5 s i n 1 8 ^{\circ}}{5 c o s 3 6 ^{\circ} - 3 s i n 1 8 ^{\circ}}$ is $\frac{a 5 - b}{c}$ , where $a, b, c$ are natural numbers and $gcd (a, c) = 1$ , then $a + b + c$ is equal to :2024 · 8 Apr · Shift 2 · Q48 · MCQ
Let the set of all $a \in R$ such that the equation $cos 2 x + a sin x = 2 a - 7$ has a solution be $[p, q]$ and $r = tan 9^{\circ} - tan 2 7^{\circ} - \frac{1}{c o t 6 3 ^{\circ}} + tan 8 1^{\circ}$ , then pqr is equal to …2024 · 27 Jan · Shift 1 · Q54 · Numerical
For $α, β \in (0, π /2)$ , let $3 sin (α + β) = 2 sin (α - β)$ and a real number $k$ be such that $tan α = k tan β$ . Then, the value of $k$ is equal to2024 · 30 Jan · Shift 2 · Q34 · MCQ
The number of solutions, of the equation $e^{s i n x} - 2 e^{- s i n x} = 2$ , is :2024 · 31 Jan · Shift 2 · Q37 · MCQ
The value of $tan 9^{\circ} - tan 2 7^{\circ} - tan 6 3^{\circ} + tan 8 1^{\circ}$ is .2023 · 6 Apr · Shift 2 · Q40 · Numerical
The value of $36 (4 cos^{2} 9^{\circ} - 1) (4 cos^{2} 2 7^{\circ} - 1) (4 cos^{2} 8 1^{\circ} - 1) (4 cos^{2} 24 3^{\circ} - 1)$ is :2023 · 8 Apr · Shift 2 · Q33 · MCQ
$96 cos \frac{π}{33} cos \frac{2 π}{33} cos \frac{4 π}{33} cos \frac{8 π}{33} cos \frac{16 π}{33}$ is equal to :2023 · 10 Apr · Shift 1 · Q33 · MCQ
Let $f (θ) = 3 (sin^{4} (\frac{3 π}{2} - θ) + sin^{4} (3 π + θ)) - 2 (1 - sin^{2} 2 θ)$ and $$S = \left\{ {\theta \in [0,\pi ]:f'(\theta ) = - {{\sqrt 3 } \over 2}}…2023 · 29 Jan · Shift 1 · Q25 · MCQ
The set of all values of $λ$ for which the equation $cos^{2} 2 x - 2 sin^{4} x - 2 cos^{2} x = λ$ has a real solution $x$ , is :2023 · 29 Jan · Shift 2 · Q31 · MCQ
If $tan 1 5^{\circ} + \frac{1}{t a n 7 5 ^{\circ}} + \frac{1}{t a n 10 5 ^{\circ}} + tan 19 5^{\circ} = 2 a$ , then the value of $(a + \frac{1}{a})$ is :2023 · 30 Jan · Shift 1 · Q30 · MCQ
$2 sin (\frac{π}{22}) sin (\frac{3 π}{22}) sin (\frac{5 π}{22}) sin (\frac{7 π}{22}) sin (\frac{9 π}{22})$ is equal to :2022 · 25 Jul · Shift 2 · Q36 · MCQ
The value of 2sin (12 $^{\circ}$ ) $-$ sin (72 $^{\circ}$ ) is :2022 · 25 Jun · Shift 2 · Q33 · MCQ
If $sin^{2} (1 0^{\circ}) sin (2 0^{\circ}) sin (4 0^{\circ}) sin (5 0^{\circ}) sin (7 0^{\circ}) = α - \frac{1}{16} sin (1 0^{\circ})$ , then $16 + α^{- 1}$ is equal to .2022 · 26 Jun · Shift 1 · Q37 · Numerical
$16 sin (2 0^{\circ}) sin (4 0^{\circ}) sin (8 0^{\circ})$ is equal to :2022 · 26 Jun · Shift 2 · Q37 · MCQ
The value of $cos (\frac{2 π}{7}) + cos (\frac{4 π}{7}) + cos (\frac{6 π}{7})$ is equal to :2022 · 27 Jun · Shift 1 · Q34 · MCQ
$α = sin 3 6^{\circ}$ is a root of which of the following equation?2022 · 27 Jun · Shift 2 · Q36 · MCQ
If cot $α$ = 1 and sec $β$ = $- \frac{5}{3}$ , where $π < α < \frac{3 π}{2}$ and $\frac{π}{2} < β < π$ , then the value of $tan (α + β)$ and the quadrant in which $α$ + $β$ lies,…2022 · 28 Jun · Shift 2 · Q40 · MCQ
If for x $\in$ $(0, \frac{π}{2})$ , log10sinx + log10cosx = $-$ 1 and log10(sinx + cosx) = $\frac{1}{2}$ (log10 n $-$ 1), n > 0, then the value of n is equal to :2021 · 16 Mar · Shift 1 · Q34 · MCQ
If 15sin4 $α$ + 10cos4 $α$ = 6, for some $α \in$ R, then the value of 27sec6 $α$ + 8cosec6 $α$ is equal to :2021 · 18 Mar · Shift 2 · Q26 · MCQ
If $e^{(c o s^{2} x + c o s^{4} x + c o s^{6} x + ...\infty) l o g_{e} 2}$ satisfies the equation t2 - 9t + 8 = 0, then the value of $\frac{2 s i n x}{s i n x + 3 c o s x} (0 < x < \frac{π}{2})$ …2021 · 24 Feb · Shift 1 · Q33 · MCQ
If 0 < x, y < $π$ and cosx + cosy $-$ cos(x + y) = $\frac{3}{2}$ , then sinx + cosy is equal to :2021 · 25 Feb · Shift 2 · Q30 · MCQ
The value of $cot \frac{π}{24}$ is :2021 · 25 Jul · Shift 2 · Q28 · MCQ
The value of $2 sin (\frac{π}{8}) sin (\frac{2 π}{8}) sin (\frac{3 π}{8}) sin (\frac{5 π}{8}) sin (\frac{6 π}{8}) sin (\frac{7 π}{8})$ …2021 · 26 Aug · Shift 2 · Q33 · MCQ
The number of integral values of 'k' for which the equation $3 sin x + 4 cos x = k + 1$ has a solution, k $\in$ R is .2021 · 26 Feb · Shift 1 · Q43 · Numerical
If $sin θ + cos θ = \frac{1}{2}$ , then 16(sin(2 $θ$ ) + cos(4 $θ$ ) + sin(6 $θ$ )) is equal to :2021 · 27 Jul · Shift 1 · Q30 · MCQ
If $tan (\frac{π}{9}), x, tan (\frac{7 π}{18})$ are in arithmetic progression and $tan (\frac{π}{9}), y, tan (\frac{5 π}{18})$ are also in arithmetic…2021 · 27 Jul · Shift 2 · Q27 · MCQ
If the equation cos4 $θ$ + sin4 $θ$ + $λ$ = 0 has real solutions for $θ$ , then $λ$ lies in the interval :2020 · 2 Sep · Shift 2 · Q25 · MCQ
If L = sin2 $(\frac{π}{16})$ - sin2 $(\frac{π}{8})$ and M = cos2 $(\frac{π}{16})$ - sin2 $(\frac{π}{8})$ , then :2020 · 5 Sep · Shift 2 · Q29 · MCQ
If $\frac{2 s i n α}{1 + c o s 2 α} = \frac{1}{7}$ and $\frac{1 - c o s 2 β}{2} = \frac{1}{10} α, β \in (0, \frac{π}{2})$ then tan( $α$ + 2 $β$ ) is…2020 · 8 Jan · Shift 2 · Q29 · Numerical
The value of $cos^{3} (\frac{π}{8}) cos (\frac{3 π}{8})$ + $sin^{3} (\frac{π}{8}) sin (\frac{3 π}{8})$ is :2020 · 9 Jan · Shift 1 · Q38 · MCQ
If $x = n = 0 \sum \infty (- 1)^{n} tan^{2 n} θ$ and $y = n = 0 \sum \infty cos^{2 n} θ$ for 0 < $θ$ < $\frac{π}{4}$ , then :2020 · 9 Jan · Shift 2 · Q31 · MCQ
If cos( $α$ + $β$ ) = 3/5 ,sin ( $α$ - $β$ ) = 5/13 and 0 < $\frac{π}{4}$ < $\frac{π}{4}$ , then tan(2 $α$ ) is equal to :2019 · 8 Apr · Shift 1 · Q40 · MCQ
The value of cos210° – cos10°cos50° + cos250° is2019 · 9 Apr · Shift 1 · Q34 · MCQ
The value of sin 10º sin30º sin50º sin70º is :-2019 · 9 Apr · Shift 2 · Q23 · MCQ
For any $θ \in (\frac{π}{4}, \frac{π}{2})$ , the expression $3 (cos θ - sin θ)^{4}$ $+ 6 (sin θ + cos θ)^{2} + 4 sin^{6} θ$ equals :2019 · 9 Jan · Shift 1 · Q25 · MCQ
The value of $cos \frac{π}{2 ^{2}} . cos \frac{π}{2 ^{3}} ..... cos \frac{π}{2 ^{10}} . sin \frac{π}{2 ^{10}}$ is -2019 · 10 Jan · Shift 2 · Q38 · MCQ
The equation y = sinx sin (x + 2) – sin2 (x + 1) represents a straight line lying in :2019 · 12 Apr · Shift 1 · Q35 · MCQ
The maximum value of 3cos $θ$ + 5sin $(θ - \frac{π}{6})$ for any real value of $θ$ is :2019 · 12 Jan · Shift 1 · Q36 · MCQ
If $5 (tan^{2} x - cos^{2} x) = 2 cos 2 x + 9$ , then the value of $cos 4 x$ is :2017 · Shift 0 · Q32 · MCQ
If m and M are the minimum and the maximum values of 4 + $\frac{1}{2}$ sin2 2x $-$ 2cos4 x, x $\in$ R, then M $-$ m is equal to :2016 · 9 Apr · Shift 1 · Q32 · MCQ
Let $f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ where $x \in R$ and $k \geq 1.$ Then $f_{4} (x) - f_{6} (x)$ equals :2014 · Shift 0 · Q43 · MCQ
The expression $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A}$ can be written as:2013 · Shift 0 · Q45 · MCQ
If $A = sin^{2} x + cos^{4} x,$ then for all real $x$ :2011 · Shift 0 · Q49 · MCQ
Let $cos (α + β) = \frac{4}{5}$ and $sin (α - β) = \frac{5}{13},$ where $0 \leq α, β \leq \frac{π}{4} .$ Then $t an 2 α$ =2010 · Shift 0 · Q47 · MCQ
Let A and B denote the statements A: $cos α + cos β + cos γ = 0$ B: $sin α + sin β + sin γ = 0$ If $cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2},$ …2009 · Shift 0 · Q45 · MCQ
If $0 < x < π$ and $cos x + sin x = \frac{1}{2},$ then $tan x$ is :2006 · Shift 0 · Q53 · MCQ
If $u = a^{2} cos^{2} θ + b^{2} sin^{2} θ + a^{2} sin^{2} θ + b^{2} cos^{2} θ$ then the difference between the maximum and minimum values of $u^{2}$ is given by :2004 · Shift 0 · Q75 · MCQ
Let $α, β$ be such that $π < α - β < 3 π$ . If $s in α + sin β = - \frac{21}{65}$ and $cos α + cos β = - \frac{27}{65}$ then the value of $\cos {{\alpha - \beta } \over…2004 · Shift 0 · Q95 · MCQ