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Trigonometric Functions and Equations

14 questions · Mathematics · JEE Main

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JEE Main
Mathematics
Trigonometric Functions and Equations

Trigonometric Functions and Equations

14 questions · Mathematics · JEE Main

If $θ \in [- 2 π, 2 π]$ , then the number of solutions of $22 cos^{2} θ + (2 - 6) cos θ - 3 = 0$ , is equal to:2025 · 2 Apr · Shift 1 · Q29 · MCQ
If $θ ϵ [- \frac{7 π}{6}, \frac{4 π}{3}]$ , then the number of solutions of $3 cosec^{2} θ - 2 (3 - 1) cosec θ - 4 = 0$ , is equal to :2025 · 2 Apr · Shift 2 · Q34 · MCQ
$The number of solutions of the equation 2 x + 3 tan x = π, x \in [- 2 π, 2 π] - {\pm \frac{π}{2}, \pm \frac{3 π}{2}} is:$ 2025 · 3 Apr · Shift 1 · Q29 · MCQ
The number of solutions of the equation $(4 - 3) sin x - 23 cos^{2} x = - \frac{4}{1 + 3}, x \in [- 2 π, \frac{5 π}{2}]$ is2025 · 3 Apr · Shift 2 · Q41 · MCQ
The number of solutions of the equation $cos 2 θ cos \frac{θ}{2} + cos \frac{5 θ}{2} = 2 cos^{3} \frac{5 θ}{2}$ in $[- \frac{π}{2}, \frac{π}{2}]$ is :2025 · 7 Apr · Shift 2 · Q38 · MCQ
The sum of all values of $θ \in [0, 2 π]$ satisfying $2 sin^{2} θ = cos 2 θ$ and $2 cos^{2} θ = 3 sin θ$ is2025 · 22 Jan · Shift 2 · Q29 · MCQ
The number of solutions of the equation $4 sin^{2} x - 4 cos^{3} x + 9 - 4 cos x = 0; x \in [- 2 π, 2 π]$ is :2024 · 1 Feb · Shift 2 · Q42 · MCQ
Let $S = {sin^{2} 2 θ : (sin^{4} θ + cos^{4} θ) x^{2} + (sin 2 θ) x + (sin^{6} θ + cos^{6} θ) = 0$ has real roots $}$ . If $α$ and $β$ be the smallest and largest elements of the…2024 · 4 Apr · Shift 2 · Q51 · Numerical
The number of solutions of $sin^{2} x + (2 + 2 x - x^{2}) sin x - 3 (x - 1)^{2} = 0$ , where $- π \leq x \leq π$ , is .2024 · 5 Apr · Shift 2 · Q59 · Numerical
Let $∣ cos θ cos (60 - θ) cos (60 + θ) ∣ \leq \frac{1}{8}, θ ϵ [0, 2 π]$ . Then, the sum of all $θ \in [0, 2 π]$ , where $cos 3 θ$ attains its maximum value, is :2024 · 9 Apr · Shift 1 · Q36 · MCQ
If $2 tan^{2} θ - 5 sec θ = 1$ has exactly 7 solutions in the interval $[0, \frac{nπ}{2}]$ , for the least value of $n \in N$ , then $\sum_{k = 1}^{n} \frac{k}{2 ^{k}}$ is equal to:2024 · 27 Jan · Shift 2 · Q43 · MCQ
If $α, - \frac{π}{2} < α < \frac{π}{2}$ is the solution of $4 cos θ + 5 sin θ = 1$ , then the value of $tan α$ is2024 · 29 Jan · Shift 1 · Q34 · MCQ
The sum of the solutions $x \in R$ of the equation $\frac{3 c o s 2 x + c o s ^{3} 2 x}{c o s ^{6} x - s i n ^{6} x} = x^{3} - x^{2} + 6$ is2024 · 29 Jan · Shift 2 · Q48 · MCQ
If $2 sin^{3} x + sin 2 x cos x + 4 sin x - 4 = 0$ has exactly 3 solutions in the interval $[0, \frac{n π}{2}], n \in N$ , then the roots of the equation $x^{2} + n x + (n - 3) = 0$ belong to :2024 · 30 Jan · Shift 1 · Q47 · MCQ