Trigonometric Angles and Equations · Mathematics · NDA

What is $\sin 9^\circ - \cos 9^\circ$ equal to?

What is the number of solutions of $(\sin \theta - \cos \theta)^2 = 2$ where $-\pi < \theta < \pi$?

What is the value of $\sin10^{\circ} \cdot \sin50^{\circ} + \sin50^{\circ} \cdot \sin250^{\circ} + \sin250^{\circ} \cdot \sin10^{\circ}$ equal to?

If $f(\theta)=\frac{1}{1+\tan \theta}$ and $\alpha+\beta=\frac{5\pi}{4}$, then what is the value of $f(\alpha) f(\beta)$?

If $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2-6x+8=0$, then what is the value of $\cos(2 \alpha+2 \beta)$?

What is the value of $\tan 65^\circ +2 \tan 45^\circ-2 \tan 40^\circ-\tan 25^\circ$?

If tan (π cos θ) = cot (π sin θ), $0<\theta<\frac{\pi}{2}$; then what is the value of $8 \sin ^2\left(\theta+\frac{\pi}{4}\right)$ ?

If $\tan \alpha=\frac{1}{7}$, $\sin \beta=\frac{1}{\sqrt{10}}$; $0<\alpha, \beta<\frac{\pi}{2}$, then what is the value of cos (α + 2β) ?

What is the period of the function?

What is the value of p + q?

What is the value of pq?

What is pq equal to ?

For how many values of x does $\frac{1}{p}$ become zero?

What is a value of sin 3x + sin 3y?

What is a value of cos³ x + cos³ y?

What is cos 2β equal to ?

What is the value of sec²γ?

What is the minimum value of x ?

At what value of A does x attain the minimum value ?

The given equation can be reduced to

If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?

What is the least value of m(θ) ?

Under what condition does m attain the least value ?

If f(x) = x(4x² - 3), then what is f(sinθ) equal to ?

What is the value of cosec$\left(−\frac{73 \pi}{3}\right)$ ?

What is the value of $\cos \left(\frac{5 \pi}{17}\right)+\cos \left(\frac{7 \pi}{17}\right)+2 \cos \left(\frac{11 \pi}{17}\right) \cos \left(\frac{\pi}{17}\right)$ ?

What is the value of tan$\left(\frac{3\pi}{8}\right)$ ?

What is cos 36° − cos 72° equal to ?

If sec x = $\frac{25}{24}$ and x lies in the fourth quadrant, then what is the value of tan x + sin x ?

What is the value of tan2 165° + cot2 165° ?

What is the value of $\sin\left(2\text{n}\pi+\frac{5\pi}{6}\right)\sin\left(2\text{n}\pi−\frac{5\pi}{6}\right)$ where n ∈ Z ?

If 1 + 2(sin x + cos x)(sin x − cos x) = 0 where 0 < x < 360°, then how many values does x take ?

What is the maximum value of 3(sin x − cos x) + 4(cos³ x − sin³ x) ?

If f(α) = $\sqrt{\sec^2\alpha−1}$, then what is $\frac{f(\alpha)+f(\beta)}{1−f(\alpha) f(\beta)}$ equal to ?

What is value of cot² 15° + tan² 15° ?

In a triangle ABC, sin A - cos B - cos C = 0. What is angle B equal to?

If $α + β = \frac{\pi}{4}$ and 2tan α = 1, then what is tan 2β equal to?

If tan (45° + θ) = 1 + sin 2θ, where $-\frac{\pi}{4}< θ <\frac{\pi}{4},$ then what is the value of cos 2θ?

Let sin 2θ = cos 3θ, where θ is acute angle. What is the value of 1 + 4 sin θ? (given that $\sin 18^\circ =\frac{\sqrt 5 - 1}{4}$)

If $\tan θ = - \frac{5}{12},$ then what can be the value of sin θ?

What is the value of $\cos^4\frac{7\pi}{8}+\cos^4\frac{5\pi}{8}?$

What is $\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)$ equal to?

If tan α + tan β = 1 - tan α.tan β, where tan α tan β ≠ 1, then which of the following is one of the values of (α + β) ?

If (1 + tan θ) (1 + tan 9θ) = 2, then what is the value of tan(10θ)?

What is the value of sin 0° + sin 10° + sin 20° + sin 30° + ⋯ + sin 360°?

What is the maximum value of the functions $f(x) = \frac{1}{\tan x+\cot x},$ where $0 < x < \frac{\pi}{2}?$

If $\tan A=\dfrac{1}{7}$, then what is cos 2A equal to?

If $\rm tan\:x=-\dfrac{3}{4}$ and x is in the second quadrant, then what is the value of sin x ⋅ cos x?

What is the value of the following?

$\rm cosec\left(\dfrac{7\pi}{6}\right)sec\left(\dfrac{5\pi}{3}\right)$

What is the value of the following?

tan 31° tan 33° tan 35° _ _ _ _ _ tan 57° tan 59°

What is the value of the following?

(sin 24° + cos 66°)(sin 24° - cos 66°)

What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?

What is $\rm \frac{1+tan^2\theta}{1+cot^2\theta}-\left(\frac{1-tan\theta}{1-cot\theta}\right)^2$equal to?

If 7 sinθ + 24 cosθ = 25, then what is the value of (sin θ + cos θ)?

If 3cosθ = 4sinθ, then what is the value of tan (45° + θ)?

The number of integer values of k, for which the equation 2sinx = 2k + 1 has a solution, is

What is cot 2x cot 4x - cot 4x cot 6x - cot 6x cot 2x equal to