Trigonometry & Inverse Trigonometry Questions - JEE

In △ABC, angle A is 120°, BC + CA = 20 and AB + BC = 21, then the length of the side BC equals:

The solution of the equation $k \cos x - 3 \sin x = k + 1$ is possible only if(JEE Main 2019)

If $4 \sin 27° = \sqrt{a + \sqrt{b}}$, then the value of $(a + b - ab + 2)^4$ must be:

Ex. 35. Statement I: Common value(s) of x satisfying the equations logsinx(secx+8)>0 and logsinxcosx+logcosxsinx=2 in (0,4π) does not exist.Statement II: On solving above trigonometric equations we have to take intersection of trigonometric chains given by secx>1 and x=nπ+π4, n∈I.

If H is the orthocentre of triangle ABC, R = circumradius and P = AH + BH + CH, then

The number of ordered pairs (x, y) satisfying |x| + |y| = 2 and sin\left(\frac{\pi x^2}{4}\right) = 1.

Given a = 6, b = 3 and $\cos(A - B) = -\frac{1}{4}$, find the area of the triangle.

Question 585. The value of M is:

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

If \sin^{-1}\frac{\alpha}{17} + \cos^{-1}\frac{1}{5} - \tan^{-1}\frac{\alpha}{36} = 0, \quad 0 < \alpha < 13, \text{ then } \sin^{-1}(\sin\alpha) + \cos^{-1}(\cos\alpha) \text{ is equal to}

11. Consider the function $f(x) = \frac{\sqrt{1 + \cos x} + \sqrt{1 - \cos x}}{\sqrt{1 + \cos x} - \sqrt{1 - \cos x}}$. If $x \in (\pi, 2\pi)$, then $f(x)$ is:

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

In an acute angled triangle ABC, given that a = 6, b = 3 and $\cos(A - B) = -\frac{1}{4}$, find angle C.

$2\sin^{-1}\sqrt{\dfrac{1-x}{2}} = \cos^{-1}(\underline{\quad})$.

For $f(x)=e^x$, $g(x)=\sin^{-1}x$, which are necessarily true?

Find the radius of the circle escribed to the triangle ABC on the side BC if $\angle NAB = 30°$; $\angle BAC = 30°$; $AB = AC = 5$.

In a $\triangle ABC$, $\angle A > \angle B$. Let $\angle A, \angle B$ satisfy the equation $3\sin x - 4\sin^3 x - k = 0$, where $0 < k < 1$, then $\angle C$ is equal to:

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60° and after 10 seconds the elevation is observed to be 30°. The uniform speed of the aeroplane in km/h is

If sin x + cos x = 1 + sin x cos x, then x is

Let ABC be a triangle such that ∠A = 45°, ∠B = 75°, then $a + c\sqrt{2}$ is equal to

If $\cos(x-y)$, $\cos x$ and $\cos(x+y)$ are in HP then $\cos x \cdot \sec\left(\frac{y}{2}\right) =$ ______

In a triangle $ABC$, it is given that $\dfrac{[ABC]}{R} = 4$, where $R$ is the circumradius. Show that $\sum_{\text{cyc}} a\cos A = 4R \prod_{\text{cyc}} \sin A$ and find $\prod_{\text{cyc}} \sin A$.

Ex. 62: If in triangle ABC, $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$, then $\sin^2 A : \sin^2 B : \sin^2 C$ is

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

If $\tan(\alpha - \beta) = \dfrac{\sin(2\beta)}{3 - \cos(2\beta)}$, then $\tan\alpha = f(\beta)$. The value of $f\!\left(\dfrac{\pi}{3}\right)$ equals:

176. If $\alpha = \sin\theta\,|\sin\theta|$ and $\beta = \cos\theta\,|\cos\theta|$ where $\theta \in \left[\dfrac{199\pi}{2},\, 100\pi\right]$, then:

The angle of elevation of tower from a point A due south of it is 30° and from a point B due west of it is 45°. If the height of the tower be 100 m, then AB =

Let $f(x) = x^4 - 8x^3 + 18x^2 - 6x + 1 - 2\sqrt{3}$, then $f\left(x = \cot\dfrac{\pi}{12}\right)$ is equal to:

If sin x₁ + sin x₂ + sin x₃ + ... + sin x₂₀₀₈ = 2008, then find the value of sin²⁰⁰⁸ x₁ + sin²⁰⁰⁸ x₂ + sin²⁰⁰⁸ x₃ + ... + sin²⁰⁰⁸ x₂₀₀₈.

In a triangle ABC if $3 \sin A + 4 \cos B = 6$; $4 \sin B + 3 \cos A = 1$ then possible value(s) of ∠C be:

If √2 cos A = cos B + cos³ B, and √2 sin A = sin B - sin³ B then sin(A - B) = ?

If 2 tan-1(1/5) - sin-1(3/5) = -cos-1(63/l), then l =

If $\cos(a+b)=\frac{3}{5}$, $\sin(a-b)=\frac{5}{13}$ and \(0

The principal value of $\cos^{-1}\left(\cos\dfrac{10\pi}{7}\right)$ is

If $ f(x) = 2\tan^{-1}x + \sin^{-1}\left(\dfrac{2x}{1+x^2}\right) $, $ x > 1 $, then $ f(t) $ is equal to

If $ \sin^{-1} x = 2\sin^{-1} a $ has a solution, then $ |a| $ satisfies:

Find the sum of squares of all values of x satisfying the equation $2\tan^{-1}x = \dfrac{\pi}{2} - 2(\pi - 2\tan^{-1}x)$ (considering all cases based on the range of x).

782. Find the number of integral values of $x$ satisfying the inequality\[\frac{\left(2^{\tan^{-1}x} - 4\right)(x-4)(x-10)}{x! - (x-1)!}

If $\sin(2\cos^{-1}\frac{1}{\sqrt{5}})+\cos(2\tan^{-1}\frac{1}{3})=\frac{p}{q}$ (coprime), units digit of $(p-q)^{2k+1}$, $k\in\mathbb{N}$ can be:

$2\tan^{-1} x = \tan^{-1}\dfrac{2x}{1-x^2}$ is true if

The inequality $\sin^{-1}(\sin 5) > x^2 - 4x$ holds if

Number of solutions of $\sin^{-1}(1-x)-2\sin^{-1}x=\pi/2$:

If $\tan^{-1}(2n) - \tan^{-1}(n) = \tan^{-1}(2n)$, then find $n$.

$\tan^{-1} x + \tan^{-1}\dfrac{2x}{1-3x^2} = \pi + \tan^{-1}\dfrac{3x - x^3}{1-3x^2}$ $(x > 0)$ is true if

$\tan^{-1}\!\left(1-x^2-\dfrac{1}{x^2}\right)+\sin^{-1}\!\left(x^2+\dfrac{1}{x^2}-1\right)$, $x\ne 0$, equals:

262. If $\sec^{-1}(x) + \tan^{-1}\sqrt{9y^2 - 1} + \sin^{-1}(x^2 + y^2) = \lambda$ has no solution, then exhaustive set of values of $\lambda$ is equal to:

Let $f: R \to \left(0, \dfrac{2\pi}{3}\right]$ defined as $f(x) = \cot^{-1}(x^2 - 4x + \alpha)$. The smallest integral value of $\alpha$ such that $f(x)$ is an into function, is equal to:

Let $f(x) = \sin x + \cos x + \tan x + \arcsin x + \arccos x + \arctan x$. If $M$ and $m$ are maximum and minimum values of $f(x)$, then their arithmetic mean is equal to

239. 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:

$4\cot^{-1} 3 + \sin^{-1}\dfrac{1}{\sqrt{5}} - \sin^{-1}\dfrac{1}{\sqrt{5}} = \underline{\quad}$.

Trigonometry & Inverse Trigonometry Questions (1013)