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## Trigonometric Functions & Equations

### Mathematics

#### Previous Years Questions

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If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 ... WB JEE 2022 The equation 6x + 8x = 10x has WB JEE 2021 Let f(x) = sin x + cos ax be periodic function. Then, WB JEE 2020$$\cos (2x + 7) = a(2 - \sin x)$$can have a real solution for WB JEE 2020 The graphs of the polynomial x2$$-$$1 and cos x intersect WB JEE 2019 If$${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$$, then the number of real values of x is WB JEE 2019 If sin6$$\theta$$+ sin4$$\theta$$+ sin2$$\theta$$= 0, then general value of$$\theta$$is WB JEE 2018 The approximate value of sin31$$^\circ$$is WB JEE 2018 The equation$$\sin x(\sin x + \cos x) = k$$has real solutions, where k is a real number. Then, WB JEE 2017 The value of cos 15$$^\circ-$$sin 15$$^\circ$$is WB JEE 2011 If$$\sin \theta + \cos \theta = 0$$and$$0
WB JEE 2011
If $$\theta$$ + $$\phi$$ = $$\pi$$/4, then (1 + tan $$\theta$$) (1 + tan $$\phi$$) is equal to
WB JEE 2011
Let $$\tan \alpha = {a \over {a + 1}}$$ and $$\tan \beta = {1 \over {2a + 1}}$$ then $$\alpha + \beta$$ is
WB JEE 2011
The number of solutions of $$2\sin x + \cos x = 3$$ is
WB JEE 2011
If $$\sin \theta = {{2t} \over {1 + {t^2}}}$$ and $$\theta$$ lies in the second quadrant, then cos $$\theta$$ is equal ...
WB JEE 2011
If $$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0$$, then the general value of $$\theta$$ is
WB JEE 2010
The value of $${{\cot 54^\circ } \over {\tan 36^\circ }} + {{\tan 20^\circ } \over {\cot 70^\circ }}$$ is
WB JEE 2010
The number of points of intersection of 2y = 1 and y = sinx, in $$-$$2$$\pi$$ $$\le$$ x $$\le$$ 2$$\pi$$ is
WB JEE 2010
The value of $${{\cot x - \tan x} \over {\cot 2x}}$$ is
WB JEE 2010
The value of $${{\sin 55^\circ - \cos 55^\circ } \over {\sin 10^\circ }}$$ is
WB JEE 2010
If $$5\cos 2\theta + 2{\cos ^2}\theta /2 + 1 = 0$$, when $$(0 ... WB JEE 2009 Simplest form of$${2 \over {\sqrt {2 + \sqrt {2 + \sqrt {2 + 2\cos 4x} } } }}$$is WB JEE 2009 In triangle ABC, a = 2, b = 3 and sin A = 2/3, thne B is equal to WB JEE 2009 The smallest value of$$5\cos \theta + 12$$is WB JEE 2009 A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3. Then the angle is WB JEE 2009$$P = {1 \over 2}{\sin ^2}\theta + {1 \over 3}{\cos ^2}\theta $$, then WB JEE 2009 The value of$$\left( {1 + \cos {\pi \over 6}} \right)\left( {1 + \cos {\pi \over 3}} \right)\left( {1 + \cos {{2\pi }...
WB JEE 2009
General solution of $$\sin x + \cos x = \mathop {\min }\limits_{a \in IR} \{ 1,{a^2} - 4a + 6\}$$ is
WB JEE 2009
The value of $$\cos 15^\circ \cos 7{1 \over 2}^\circ \sin 7{1 \over 2}^\circ$$ is
WB JEE 2009
The equation $$\sqrt 3 \sin x + \cos x = 4$$ has
WB JEE 2009
The value of $$\cos {\pi \over {15}}\cos {{2\pi } \over {15}}\cos {{4\pi } \over {15}}\cos {{8\pi } \over {15}}$$ is...
WB JEE 2008
The principal value of $${\sin ^{ - 1}}\tan \left( { - {{5\pi } \over 4}} \right)$$ is
WB JEE 2008
If $$\tan \left( {{{\alpha \pi } \over 4}} \right) = \cot \left( {{{\beta \pi } \over 4}} \right)$$ then
WB JEE 2008
The equation $$\sqrt 3 \sin x + \cos x = 4$$ has
WB JEE 2008

## Subjective

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Find the values of x, ($$-$$ $$\pi$$, ...
WB JEE 2010
Prov that the equation $$\cos 2x + a\sin x = 2a - 7$$ possesses a solution if 2 $$\le$$ a $$\le$$ 6.
WB JEE 2010
Show that $${{\sin \theta } \over {\cos 3\theta }} + {{\sin 3\theta } \over {\cos 9\theta }} + {{\sin 9\theta } \over {\... WB JEE 2009 Find the general solution of$$\sec \theta + 1 = (2 + \sqrt 3 )\tan \theta .
WB JEE 2008

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