Trigonometry Questions (1127)

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

Let $x_1$ and $x_2$ ($x_1 > x_2$) are the roots of the equation $9^{\log_9(x^2-4x+5)} = x-1$, then the value of $\tan(x_1)\pi + \sec(x_2)\pi$ is:

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.

$\tan^{-1}\left(\tan\dfrac{5\pi}{6}\right)+\cos^{-1}\left(\cos\dfrac{13\pi}{6}\right)=$

If $r_1$ and $r_2$ are the remainder when $f(x)=4x^3+3x^2-12x+a$ is divided by $(x-1)$ and $(x+2)$, and $2r_1+r_2=6$, then $a=$

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

The least positive value of $x$ satisfying the equation $\dfrac{\sin x}{\cos 3x} + \dfrac{\sin 3x}{\cos 9x} + \dfrac{\sin 9x}{\cos 27x} = 0$ 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

Let $x=\sin1°$. The value of $\dfrac{1}{\cos0°\cos1°}+\dfrac{1}{\cos1°\cos2°}+\cdots+\dfrac{1}{\cos44°\cos45°}$ is

The maximum value of the function $f(x) = \dfrac{4\cot^{-1}x}{\pi} - \dfrac{\pi}{4\cot^{-1}(-x)}$ occurs at $x$ equal to

If $(\sin^{-1}x)^2 + (\sin^{-1}y)^2 + 2\sin^{-1}x\sin^{-1}y = \pi^2$, then $x^2 + y^2$ is equal to: