Trigonometric Equations

The number of solutions in \([0,2 \pi]\) of the equation \(16^{\sin ^2 x}+16^{\cos ^2 x}=10\) is

The principal solutions of the equation \(\sec x+\tan x=2 \cos x\) are

The general solution of the equation \(3 \sec ^2 \theta=2 \operatorname{cosec} \theta\) is

If \((1+\sqrt{1+x}) \tan x=1+\sqrt{1-x}\), then \(\sin 4 x\) is

The solution of \(\sin x+\sin 5 x=\sin 3 x\) in \((0, \pi / 2)\) are

If general solution of \(\cos ^2 \theta-2 \sin \theta+\frac{1}{4}=0\) is \(\theta=\frac{\mathrm{n} \pi}{\mathrm{A}}+(-1)^{\mathrm{n}} \frac{\pi}{\mathrm{B}}, \mathrm{n} \in \mathrm{Z}\), then \(\mathrm{A}+\mathrm{B}\) has the

The solution set of \(8 \cos ^2 \theta+14 \cos \theta+5=0\), in the interval \([0,2 \pi]\), is

If the general solution of the equation \(\frac{\tan 3 x-1}{\tan 3 x+1}=\sqrt{3}\) is \(x=\frac{\mathrm{n} \pi}{\mathrm{p}}+\frac{7 \pi}{\mathrm{q}}, \mathrm{n}, \mathrm{p}, \mathrm{q}, \in \mathrm{Z}\), then \(\frac{p}{q}\) is

If \(\cos x+\cos y-\cos (x+y)=\frac{3}{2}\), then

The number of solutions of \(\tan x+\sec x=2 \cos x\) in \([0,2 \pi]\) are

The number of possible solutions of \(\sin \theta+\sin 4 \theta+\sin 7 \theta=0, \theta \in(0, \pi)\) are

If \(3 \sin \theta=2 \sin 3 \theta\) and \(0< \theta<\pi\), then \(\sin \theta=\)

The principal solutions of \(\cot x=\sqrt{3}\) are

\(2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)\), then \(\tan \theta=\)

If \(\theta+\phi=\alpha\) and \(\tan \theta=k \tan \phi(\) where \(K>1)\), then the value of \(\sin (\theta-\phi)\) is

The number of solutions of cos2\(\theta\) = sin\(\theta\) in (0, 2\(\pi\)) are

If \(x \in\left(0, \frac{\pi}{2}\right)\) and \(x\) satisfies the equation \(\sin x \cos x=\frac{1}{4}\), then the values of \(x\) are

The principal solutions of \(\sqrt{3} \sec x+2=0\) are

The principal solutions of $\cot x=\sqrt{3}$ are

If $2 \cos ^2 \theta+3 \cos \theta=2$, then permissible value of $\cos \theta$ is

\(\tan A+2 \tan 2 A+4 \tan 4 A+8 \cot 8 A=\)

The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x=\frac{1}{4}$ are ..........

Which of the following equations has no solution?

The number of solutions of $\sin ^2 \theta=\frac{1}{2}$ in $[0, \pi]$ is ..........