Trigonometric Functions & Equations · Mathematics · WB JEE

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 + ...

$$P = {1 \over 2}{\sin ^2}\theta + {1 \over 3}{\cos ^2}\theta $$, 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

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

The value of cos 15$$^\circ$$ $$-$$ sin 15$$^\circ$$ is

The expression $$\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$$ is

If $$0...

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 ...

The equation 6x + 8x = 10x has

$$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for

Let f(x) = sin x + cos ax be periodic function. Then,

If $${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$$, then the number of real values of x is

The graphs of the polynomial x2 $$-$$ 1 and cos x intersect

The approximate value of sin31$$^\circ$$ is

If sin6$$\theta$$ + sin4$$\theta$$ + sin2$$\theta$$ = 0, then general value of $$\theta$$ is

The equation $$\sin x(\sin x + \cos x) = k$$ has real solutions, where k is a real number. Then,

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

The area enclosed by $$y = \sqrt {5 - {x^2}} $$ and $$y = |x - 1|$$ is

Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P $$ \in $$ S, such that the sum of the distance of P from (8, 0) a...

If x is a positive real number different from 1 such that logax, logbx, logcx are in AP, then

If z1, z2, z3 are imaginary numbers such that $$|{z_1}|\, = \,|{z_2}|\, = \,|{z_3}|\, = \,\left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z...

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

$$1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta $$ equals

Let $$Q = \left[ {\matrix{ {\cos {\pi \over 4}} & { - \sin {\pi \over 4}} \cr {\sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr ...

If the function f : R $$ \to $$ R is defined by f(x) = (x2 + 1)35, $$\forall $$ x$$ \in $$R, then f is

The value of $$\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}$$ is

The smallest positive root of the equation tan x $$-$$ x = 0 lies in

The points ($$-$$a, $$-$$b), (a, b), (0, 0) and (a2, ab), a $$ \ne $$ 0, b $$ \ne $$ 0 are always

The locus of the point of intersection of the straight lines $${x \over a} + {y \over b} = K$$ and $${x \over a} - {y \over b} = {1 \over K}$$, where ...

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at

Angle between the planes x + y + 2z = 6 and 2x $$-$$ y + z = 9 is

If f(x) is an odd differentiable function defined on ($$-$$$$\infty $$, $$\infty $$) such that f'(3) = 2, then f'($$-$$3) is equal to

$$\int {{{\log \sqrt x } \over {3x}}} dx$$ is equal to

The equation x3 $$-$$ yx2 + x $$-$$ y = 0 represents

The number of points at which the function f(x) = max {a $$-$$ x, a + x, b}, $$-$$ $$\infty $$ < x < $$\infty $$, 0 < a < b cannot be diff...

For non-zero vectors a and b, if | a + b | < | a $$-$$ b |, then a and b are

If the matrix $$A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr } } \right]$$, then $${A^n} = ...

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}(...

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, ($$-$$ $$\pi$$, ...

If the first and (2n $$-$$ 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then always

If the parabola x2 = ay makes an intercept of length $$\sqrt {40} $$ units on the line y $$-$$ 2x = 1, then, a is equal to