Inverse Trigonometry Questions - JEE

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

If \(0 \leq x

The sum of all values of $\theta \in \left(0, \dfrac{\pi}{2}\right)$ satisfying $\sin^2 2\theta + \cos^4 2\theta = \dfrac{3}{4}$ is:

If \(0

Suppose 3\sin^{-1}(\log_2 x) + \cos^{-1}(\log_2 y) = \frac{\pi}{2} and \sin^{-1}(\log_2 x) + 2\cos^{-1}(\log_2 y) = \frac{11\pi}{6} then the value of x^2 + y^2 equals

If $\cos^{-1}\!\sqrt{p}+\cos^{-1}\!\sqrt{1-p}+\cos^{-1}\!\sqrt{1-q}=\dfrac{3\pi}{4}$, then $q$ is

If $\cos^{-1}(2x^2-1)=2\pi-2\cos^{-1}x$, then:

Let $\frac{5}{6}\cos^{-1}\sqrt{\dfrac{3}{3+\pi^2}}+\frac{1}{3}\sin^{-1}\dfrac{2\sqrt{3}\pi}{3+\pi^2}+\frac{1}{6}\tan^{-1}\dfrac{\sqrt{3}}{\pi}=a$ and $\cos^{-1}\!\left[\frac{13}{40}\cos\!\left(\cot^{-1}\frac{5}{12}\right)+\frac{13}{32}\sin\!\left(\cos^{-1}\frac{5}{13}\right)\right]=b$. Then $\csc\!\left(\displaystyle\int_b^a\left[\frac{\tan x}{\sqrt{3}}\right]dx\right)$ is ($[\cdot]$ = GIF)

Find the range of f(x) = \sin^{-1} x + \tan^{-1} x + \sec^{-1} x

Find the number of solutions of $\cos x = |1 + \sin x|$, \(0

$\text{cosec}^{-1}(\cos x)$ exists if:

If a = \tan x, then the value of \cot\left(\frac{\pi}{4} - a\right) is

If a root of the equation $n^2\sin^2 x + 2\sin x - (2n+1) = 0$ lies in $[0, \frac{\pi}{2}]$, find the minimum positive integer value of $n$.

In $\triangle ABC$, if incircle touches the sides $AB$, $BC$ and $CA$ at $P$, $Q$ and $R$ respectively and $s - a = 3$, $s - b = 5$ and $s - c = 7$, then area of the quadrilateral $QCRI$ is, where $I$ is incentre of $\triangle ABC$:[Note: Symbols used have usual meaning in $\triangle ABC$.]

Inverse Trigonometry Questions (1043)