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Trigonometric Functions and Equations question

2012 · Shift 1 · Q21

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2012 · Shift 1 · Q21

Trigonometric Functions and Equations question

2012 · Shift 1 · Q21

JEE AdvancedMathematicsTrigonometric Functions and EquationsMultiple correct+4 / −1

Let

\theta ,\,\varphi \, \in \,\left[ {0,2\pi } \right]

be such that

2\cos \theta \left( {1 - \sin \,\varphi } \right) = {\sin ^2}\theta \,\,\left( {\tan {\theta \over 2} + \cot {\theta \over 2}} \right)\cos \varphi - 1,\,\tan \left( {2\pi - \theta } \right) \gt 0

and

- 1 \lt \sin \theta \, \lt - {{\sqrt 3 } \over 2},

then

\varphi

cannot satisfy

A
$0 \lt \varphi \lt {\pi \over 2}$
B
${\pi \over 2} \lt \varphi \lt {{4\pi } \over 3}$
C
${{4\pi } \over 3} \lt \varphi \lt {{3\pi } \over 2}$
D
${{3\pi } \over 2} \lt \varphi \lt 2\pi$

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