Trigonometry Questions - JEE

If $\dfrac{1}{2}\sin^{-1}\!\left(\dfrac{3\sin 2\alpha}{5 + 4\cos 2\alpha}\right) = \tan^{-1} x$, then the possible value of $x$ is:

The period of the function $f(x) = \sin^4 x + \cos^4 x$ is:

In $\triangle ABC$, circumradius is 3 and inradius is 1.5 units. If the value of $a\cot^2 A + b^2\cot^3 B + c^3\cot^4 C$ is $m\sqrt{n}$ where m and n are prime numbers, then find the value of $\left(\dfrac{m-1}{n}\right)$.

If $\dfrac{p-1}{2p+3} = \sin^2\theta + 2\cos\theta + 1$ $\forall\, \theta \in R$, then $p$ must lie in the interval:

9. Consider a triangle ABC such that $\cot A + \cot B + \cot C = \cot \theta$. The possible value of $\theta$ is:

$\sin^{-1}\sqrt{\dfrac{x}{x+y}} = \tan^{-1}(\underline{\quad})$.

The value of $\cos^2 10° - \cos 10° \cos 50° + \cos^2 50°$ is

The least value of $\csc^2 x + 25\sec^2 x$ is

If $\tan A$ and $\tan B$ are the roots of the quadratic equation, $3x^2-10x-25=0$, then the value of $3\sin^2(A+B)-10\sin(A+B)\cos(A+B)-25\cos^2(A+B)$ is

Given a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid-point D of AC subtends an angle 30° at B. Find the height of the lamp-post.

Given $\cos^{-1}\left(\dfrac{2}{3x}\right) + \cos^{-1}\left(\dfrac{3}{4x}\right) = \dfrac{\pi}{2}$Find the value of $x$.

The value of $\sin\sqrt{x^2 - \frac{\pi^2}{36}}$ lies in the interval

Maximum possible perimeter of the triangle is :

Given $\tan\theta = \dfrac{-4}{3}$, find $\sin\theta$.

If $y = \sqrt{t} + \sqrt{(\pi/2) - t}$ where $t = \sin^{-1} x$, $x \in [0, \pi/2]$, then the maximum value of $y$ is:

If $p = \cos 55°$, $q = \cos 65°$ and $r = \cos 175°$, then the value of $\dfrac{1}{p} + \dfrac{1}{q} + \dfrac{r}{pq}$ is equal to:

173. If $\cos x + \cos^2 x = 1$. Let $E = \sin^{12} x + 3\sin^{10} x + 3\sin^8 x + \sin^6 x + 2$, then the value of $\log_{\tan\frac{\pi}{3}} E$ is:

Find the value of $x$, if $\tan^{-1}\dfrac{yz}{rx} + \tan^{-1}\dfrac{zx}{ry} + \tan^{-1}\dfrac{xy}{rz} = x^\circ$ and $r^2 = x^2 + y^2 + z^2$.

If a, b, c be the sides of a triangle ABC and the roots of the equation $a(b-c)x^2 + b(c-a)x + c(a-b) = 0$ are equal, then $\sin^2\left(\dfrac{A}{2}\right), \sin^2\left(\dfrac{B}{2}\right), \sin^2\left(\dfrac{C}{2}\right)$ are in

Given that the roots of the equation $2x^2 - 10x - 25 = 0$ are $\tan A$ and $\tan B$, find the value of $3\sin^2(A+B) - 10\sin(A+B)\cos(A+B) - 25\cos^2(A+B)$.

If $\displaystyle\sum_{r=1}^{100} \sin^{-1}\!\left(\frac{1}{\sqrt{r^2+1}\sqrt{r^2+2r+2}}\right)$ is equal to $\tan^{-1}\!\left(\dfrac{p}{q}\right)$ where $p$ and $q$ are co-prime, then the value of $(p+q)$ is equal to:

160. If $\cos^{-1}\!\left(\dfrac{2}{3x}\right) + \cos^{-1}\!\left(\dfrac{3}{4x}\right) = \dfrac{\pi}{2}$ $\left(x > \dfrac{3}{4}\right)$, then $x$ is equal to:

If $\cos A = \cos B$ and $\sin A = \sin B$ then

If in a triangle ABC; ∠C = π/8; a = √2; b = √(2 + √2) then the measure of ∠A can be:

If A > 0, B > 0 and A + B = π/6, then the maximum value of tan A + tan B is:

If \(\frac{1}{3} \leq \sin x a.

Let $\sec x + \tan x = \frac{22}{7}$, where \(0

If $\cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi$, then $xy+yz+zx=$

$\displaystyle\lim_{n\to\infty}\sum_{r=1}^{n}\tan^{-1}\!\frac{2r+1}{r^4+2r^3+r^2+1}=$

In a triangle $ABC$, $2ca\sin\dfrac{A-B+C}{2}$ is equal to

$\sin^{-1}(\sin 5)>x^2-4x$ holds for:

If $a$ and $b$ are the roots of the equation $4x^2 - 3x + a = 0$, sin $A + \cos A + \tan A + \cot A + \sec A + \cos A = 7$ and $0 < A < \frac{\pi}{2}$, then the value of $a$ must be

The value of the expression $\dfrac{\sin^2\dfrac{2\pi}{7} + \sin^2\dfrac{4\pi}{7} + \sin^2\dfrac{\pi}{7}}{\sin^2\dfrac{\pi}{7} + \sin^2\dfrac{2\pi}{7} + \sin^2\dfrac{4\pi}{7}}$ is equal to:

Solve $\theta = \tan^{-1}(2\tan^2\theta) - \frac{1}{2}\sin^{-1}\left(\frac{3\sin 20}{5 + 4\cos 20}\right)$.

Solve for $x$: $\tan^{-1} x + \tan^{-1}(1-x) = \cot^{-1}\frac{7}{9}$, where $x \in (0,1)$.

Two poles of heights 20 m and 80 m are standing on a horizontal ground. The height (in metres) of the point of intersection of the lines joining the top of each pole to the foot of the other pole is:

If $|2x + \sin^2 a| + |2x + 3 + 2\sin a| = 0$ and $4\lambda^2 = 1$, find $4\lambda^2$.

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 min from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then, the time taken (in minutes) by him, from B to reach the pillar, is

If $\sin^{-1}\!\sqrt{x/2}+\sin^{-1}\!\sqrt{1-x/4}+\tan^{-1}y=\frac{2\pi}{3}$, then which are true?

Let a and b be the lengths of the legs of a right triangle with the following properties: (a) All 3 sides of the triangle are integers. (b) The perimeter of the triangle is numerically equal to area of the triangle, it is given that a < b. The number of ordered pairs (a, b) will be :

The value of $S = \dfrac{\sin^2\dfrac{2\pi}{7}}{\sin^2\dfrac{\pi}{7}} + \dfrac{\sin^2\dfrac{4\pi}{7}}{\sin^2\dfrac{2\pi}{7}} + \dfrac{\sin^2\dfrac{\pi}{7}}{\sin^2\dfrac{4\pi}{7}}$ is:

If ABCD is a cyclic quadrilateral then $\cos A + \cos B + \cos C + \cos D$ is equal to

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30°. The height of the tower is

A $150\left(\sqrt{3}+1\right)$ ft.

Which are correct?(A) $\cot^{-1}x=\tan^{-1}(1/x)\ \forall x\in\mathbb{R}\setminus\{0\}$(B) $f(x)=\text{sgn}(e^x)$ is into(C) $f:\mathbb{R}^+\to\mathbb{R},\,f(x)=\sin x+x$ is odd(D) $f(x)=e^x/e^{[x]}$ is periodic

$\sin[\cot^{-1}\{\tan(\cos^{-1} x)\}]$ is equal to

The number of possible solutions of x such that $\sin^2 x + \cos^2 x = 1$ is:

Let $a \in \left(\dfrac{-\pi}{2}, \dfrac{\pi}{2}\right)$ such that $\tan^{-1}\!\left(\dfrac{\tan\alpha}{3 + 2\tan^2\alpha}\right) + \tan^{-1}\!\left(\dfrac{2\tan\alpha}{3}\right) = \dfrac{\pi}{12}$, then $\alpha$ equals:

811. In $\triangle ABC$, if $\sin A \sin B \sin C + \cos A \cos B = 1$ then the value of $\cos^2 A + \sin^2 B + 2\sin^2 \dfrac{C}{2}$ is:

If \(2\le a

Trigonometry Questions (1127)