Inverse Trigonometry Questions - JEE

$\sin^{-1}(3x - 4x^3) = \lambda \sin^{-1} x$ then $\lambda = \underline{\quad}$.

If inside triangle ABC, a, b, c and angle A are given and \(c\sin A

The value of $\sqrt{\sin^2\frac{2\pi}{11} - \cos\frac{8\pi}{11}}$ is equal to

If $P = \frac{\tan(3^n + 10) - \tan\theta}{\cos(3^n \theta)}$ and $Q = \text{(expression)}$, then

Given, $a^2 + 2a + \csc^2\frac{x}{2} - (a+x) = 0$, then which of the following holds good?

Let f(x) = sin²³x + cos²²x and g(x) = 1 − $\frac{1}{2}$ tan⁻¹|x|. The number of values of x in interval [−100°, 200°] satisfying the equation f(x) = sgn(g(x)), is 5a. Then, a is equal to ……

The complete set of values of a for which the function f(x) = \tan^{-1}(x^2 - 18x + a) \geq 0, \forall x \in \mathbb{R}, is

The value of $4\cos 20° - 3\cot 20°$ is

If in a triangle ABC, cot A}{2} + cot B}{2} + cot C}{2} = X cot A}{2} cot B}{2} cot C}{2}, then find the value of X.

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

The maximum value of $4\sin^2 x + 3\cos^2 x + \sin\left(\frac{x}{2}\right) + \cos\left(\frac{x}{2}\right)$ is

The sides of a triangle are $\sin\alpha$, $\cos\alpha$ and $\sqrt{1 + \sin\alpha\cos\alpha}$ for some \(0

If $4x^3 - 3x - p = 0$, where $-1 \leq p \leq 1$ has a unique root in $[-1, 1]$, then the root is

If cot θ + cot(π/4 - θ) = 2, then the general value of θ is

Example 42: The set of values of $X \in \mathbb{R}$ such that $\tan^2 \theta + \sec \theta = X$ holds for some $\theta$ is

Find the value of $\sin 20° + \cos 40° + \sin 50° + \tan 70° + \cot 80°$.

The minimum value of $\sin^4 a + \sin^4 b + \sin^4 g$, where $a, b, g$ are real positive angles satisfying $a + b + g = \pi$, is

Let $ABC$ be a right angled triangle at $C$. If the inscribed circle touches the side $AB$ at $D$ and $(AD)(BD) = 11$, then find the area of $\triangle ABC$.

Ex. 84: If x sin³θ + y cos³θ = sin θ cos θ and x sin θ - y cos θ = 0, then (x, y) lie on

D, E and F are the middle points of the sides of the triangle ABC, then

x_1 and x_2 are two positive values of x for which 2 \cos x, |\cos x|, and 3\sin^2 x - 2 are in GP. The minimum value of |x_1 - x_2| is equal to

If a = \sin\frac{\pi}{18} \sin\frac{7\pi}{18} \sin\frac{13\pi}{18}, then a is equal to

The sum \frac{1}{\sin 45° \sin 46°} + \frac{1}{\sin 47° \sin 48°} + \ldots + \frac{1}{\sin 133° \sin 134°} is equal to

The value of $\text{cosec}10°-\sqrt{3}\sec10°$ is equal to:

Let $u = \cot^{-1}\sqrt{\cos 2\theta} - \tan^{-1}\sqrt{\cos 2\theta}$, then the value of $\sin u$ is

Statement I: Let $f(x) = \sin^{-1}\left(\frac{2x}{1+x^2}\right)$. Then $f'(2) = -\frac{2}{5}$Statement II: $\sin^{-1}\left(\frac{2x}{1+x^2}\right) = \pi$

If $\cot^{-1}\left(\frac{n^2 - 10n + 21}{\pi}\right) > \frac{\pi}{6}$, $n \in \mathbb{N}$, then find the maximum value of $n$.

The set of values of x, satisfying the equation $\tan^2(\sin^{-1} x) > \frac{1}{2}$

Number of values of $x$ satisfying the equation $\cos(3\arccos(x-1)) = 0$ is equal to

Simplify: $1 + \tan^2(\tan^{-1} x) - (\sec^2(\sec^{-1} x) - 1)$

The value of $\tan \frac{\pi}{7} \tan \frac{2\pi}{7} \tan \frac{3\pi}{7}$ is

If the mapping f(x) = mx + c, m > 0 maps [-1, 1] onto [0, 2], then \tan\left(\tan^{-1}\frac{1}{7} + \cot^{-1}8 + \cot^{-1}18\right) is equal to

If $\cos^{-1}x - \cos^{-1}\left(\frac{y}{2}\right) = a$, then $4x^2 - 4xy\cos a + y^2$ equals

If the range of the function $f(x) = \tan^{-1}(3x^2 + bx + c)$ is $\left[0, \frac{\pi}{2}\right)$ (domain is $\mathbb{R}$), then:

Points $D, E$ are taken on the side $BC$ of $\triangle ABC$, such that $BD = DE = EC$ and let $\angle BAD = x, \angle DAE = y, \angle EAC = z$; then $\frac{\sin(x+y)\sin(y+z)}{\sin x \sin z} =$

Sides AB and AC in an equilateral triangle ABC with side length 3 is extended to form two rays from point A. Point P is chosen outside the triangle ABC and between the two rays such that ∠ABP + ∠BCP = 180°. If the maximum length of CP is M, then $M^2/2$ is equal to:

If the circumradius of ∆ABC is 3 units and its area is 6 square units, and ∆DEF is formed by joining the feet of perpendiculars drawn from A, B, C on sides BC, CA, AB respectively, find the perimeter of ∆DEF.

The number of solutions of the system of equations:$2\sin^2 x + \sin^2 2x = 2$$\sin 2x + \cos 2x = \tan x$in $[0, 4\pi]$ satisfying $2\cos 2x + \sin x \le 2$ is:

If $A, B, C, D$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$, then the value of $4\sin\frac{A}{2}+3\sin\frac{B}{2}+2\sin\frac{C}{2}+\sin\frac{D}{2}$ is equal to:

12. If the value of $f\left(\frac{\pi}{3}\right) = a + b\sqrt{c}$ where $a, b, c \in \mathbb{N}$, then the value of $a + b + c$ is:

If \frac{\sin^2 2x + 4\sin 4x - 4\sin 2x \times \cos 2x}{4 - \sin^2 2x - 4\sin 2x} = \frac{1}{9} and 0 , then the value of x is:

In $\triangle A_4B_4C_4$, find the value of $\angle A_4$

If $A = \sum_{r=1}^{3}\cos\frac{2r\pi}{7}$ and $B = \sum_{r=1}^{3}\cos\frac{2r\pi}{7}$, then:

In a right angled triangle ABC with $A = \dfrac{\pi}{2}$, a circle is drawn touching the side AB, AC and in circle of the triangle. Its radius is equal to

Let incircle of radius $4$ units of a triangle $ABC$ touches the side $BC$ at $D$. If $BD = 6, DC = 8$ and $\Delta$ be the area of triangle, then $\sqrt[4]{\Delta - 3}$ = _______.

The total number of solutions of $\tan\{x\} = \cot\{x\}$ ; where $\{x\}$ denotes the fractional part of $x$ in $[0, 2\pi)$ is _______.

If $\sin x + \sin^2 x + \sin^3 x = 1$, then $\cos^6 x - 4\cos^4 x + 8\cos^2 x$ = _______.

If $\tan\left(\frac{2\pi}{3} - x\right) = \frac{\sin\frac{2\pi}{3} - \sin x}{\cos\frac{2\pi}{3} - \cos x}$ where $0 < x < \frac{3\pi}{2}$, and the values of $x$ are $x_1$ and $x_2$, then the value of $\frac{12}{\pi}|x_2 - x_1|$ is

If $10\sin^4 u + 15\cos^4 u = 6$ and the value of $9\cos\sec^4 u + 8\sec^4 u$ is $S$, then find the value of $\frac{S}{25}$

If $\sum_{r=1}^{q}\frac{\tan 2^{r-1}}{\cos 2^r} = \tan p^n - \tan q$, then find the value of $(p + q)$

Inverse Trigonometry Questions (1043)