The equation $$\sqrt 3 \sin x + \cos x = 4$$ has
If $$\tan \left( {{{\alpha \pi } \over 4}} \right) = \cot \left( {{{\beta \pi } \over 4}} \right)$$ then
The principal value of $${\sin ^{ - 1}}\tan \left( { - {{5\pi } \over 4}} \right)$$ is
The value of $$\cos {\pi \over {15}}\cos {{2\pi } \over {15}}\cos {{4\pi } \over {15}}\cos {{8\pi } \over {15}}$$ is
The equation $$\sqrt 3 \sin x + \cos x = 4$$ has
The value of $$\cos 15^\circ \cos 7{1 \over 2}^\circ \sin 7{1 \over 2}^\circ $$ is
General solution of $$\sin x + \cos x = \mathop {\min }\limits_{a \in IR} \{ 1,{a^2} - 4a + 6\} $$ is
The value of $$\left( {1 + \cos {\pi \over 6}} \right)\left( {1 + \cos {\pi \over 3}} \right)\left( {1 + \cos {{2\pi } \over 3}} \right)\left( {1 + \cos {{7\pi } \over 6}} \right)$$ is
$$P = {1 \over 2}{\sin ^2}\theta + {1 \over 3}{\cos ^2}\theta $$, then
A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3. Then the angle is
The smallest value of $$5\cos \theta + 12$$ is
In triangle ABC, a = 2, b = 3 and sin A = 2/3, thne B is equal to
Simplest form of $${2 \over {\sqrt {2 + \sqrt {2 + \sqrt {2 + 2\cos 4x} } } }}$$ is
If $$5\cos 2\theta + 2{\cos ^2}\theta /2 + 1 = 0$$, when $$(0 < \theta < \pi )$$, then the values of $$\theta$$ are
The value of $${{\sin 55^\circ - \cos 55^\circ } \over {\sin 10^\circ }}$$ is
The value of $${{\cot x - \tan x} \over {\cot 2x}}$$ is
The number of points of intersection of 2y = 1 and y = sinx, in $$-$$2$$\pi$$ $$\le$$ x $$\le$$ 2$$\pi$$ is
The value of $${{\cot 54^\circ } \over {\tan 36^\circ }} + {{\tan 20^\circ } \over {\cot 70^\circ }}$$ is
If $$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0$$, then the general value of $$\theta$$ is
If $$\sin \theta = {{2t} \over {1 + {t^2}}}$$ and $$\theta$$ lies in the second quadrant, then cos $$\theta$$ is equal to
The number of solutions of $$2\sin x + \cos x = 3$$ is
Let $$\tan \alpha = {a \over {a + 1}}$$ and $$\tan \beta = {1 \over {2a + 1}}$$ then $$\alpha + \beta $$ is
If $$\theta$$ + $$\phi$$ = $$\pi$$/4, then (1 + tan $$\theta$$) (1 + tan $$\phi$$) is equal to
If $$\sin \theta + \cos \theta = 0$$ and $$0 < \theta < \pi $$, then $$\theta$$ =
The value of cos 15$$^\circ$$ $$-$$ sin 15$$^\circ$$ is
Let $f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)$, then
If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}, 0<\theta, \phi<\frac{\pi}{4}$, then $\cot (2 \theta)$ has the value
The expression $$\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$$ is
If $$0< \theta<\frac{\pi}{2}$$ and $$\tan 3 \theta \neq 0$$, then $$\tan \theta+\tan 2 \theta+\tan 3 \theta=0$$ if $$\tan \theta \cdot \tan 2 \theta=\mathrm{k}$$ where $$\mathrm{k}=$$
If $$A$$ and $$B$$ are acute angles such that $$\sin A=\sin ^2 B$$ and $$2 \cos ^2 A=3 \cos ^2 B$$, then $$(A, B)=$$
If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is
(Here $$n \in N$$)
If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2$$, then the maximum value of $$(\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})$$ is given by
Find the general solution of $$\sec \theta + 1 = (2 + \sqrt 3 )\tan \theta $$.
Show that $${{\sin \theta } \over {\cos 3\theta }} + {{\sin 3\theta } \over {\cos 9\theta }} + {{\sin 9\theta } \over {\cos 27\theta }} = {1 \over 2}(\tan 27\theta - \tan \theta )$$
Prov that the equation $$\cos 2x + a\sin x = 2a - 7$$ possesses a solution if 2 $$\le$$ a $$\le$$ 6.
Find the values of x, ($$-$$ $$\pi$$, < x < $$\pi$$, x $$\ne$$ 0) satisfying the equation, $${8^{1 + |\cos x| + |{{\cos }^2}x| + ......\infty }} = {4^3}$$.
If the equation $\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0$ has a solution, the $p$ must lie in the interval
If $0 \leq a, b \leq 3$ and the equation $x^2+4+3 \cos (a x+b)=2 x$ has real solutions, then the value of $(a+b)$ is
The solution set of the equation $\left(x \in\left(0, \frac{\pi}{2}\right)\right) \tan (\pi \tan x)=\cot (\pi \cot x)$, is