Trigonometric Equations

Number of solutions for $\tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2 + x + 1} = \dfrac{\pi}{2}$ is:

The equation $\sin^4 x + \cos^4 x + \sin 2x + \alpha = 0$ is solvable for:

Solve: $ 2\sin^{2}\theta - 3\sin\theta - 2 = 0$

The solution of $\sin x +1 = \cos x $ such that $0\leq x\leq 2\pi$ is

Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and $Q = \{\theta : \sin\theta + \cos\theta = \sqrt{2}\sin\theta \}$ be two sets. Then

The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is

Let S be the set $\{a\in Z^+:a\leq100\}$.If the equation $[tan^2 x]-tan x - a = 0$ has real roots (where [ . ] is the greatest integer function), then the number of elements is S is

The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x

Number of real solutions of the equation $\sin\!\left(e^x\right) = 5^x + 5^{-x}$ is

If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =

If $\frac{tanx}{2}=\frac{tanx}{3}=\frac{tanx}{5}$ and x + y + z = π, then the value of tan²x + tan²y + tan²z is

Solve the equation sin² x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π

If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$

If |k|=5 and 0° ≤ θ ≤ 360°, then the number of distinct solutions of 3cos⁡θ + 4sin⁡θ = k is

If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =

The general value of $\theta$, satisfying the equation $\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$