Trigonometric Identities - Practice Questions & MCQ

If then for all real

The sum of all values of $\theta \epsilon(0, \pi / 2)$ satisfying $\sin ^2 2 \theta+\cos ^4 2 \theta=3 / 4$ is:

For $\alpha, \beta \in(0, \pi / 2)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $\mathrm{k}$ be such that $\tan \alpha=\mathrm{k} \tan \beta$. Then, the value of $\mathrm{k}$ is equal to

$\sqrt{1-\sin^{2}\theta}$  equals

If $\tan \theta=\frac{4}{5}$, find $\sec \theta$ ( $\theta$ is in 4th quadrant)

$\cos ^{-1} x=\tan ^{-1} x$, then $\cos ^2 \theta=$ ?

$\operatorname{Sec}^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$ is equal to

If the perimeter of a sector of a circle, of area $25 \pi$ square cms is 20 cm , then area of a sector is

If $\sin \theta+\sin ^2 \theta=1$, then the value of $\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta-1$ is equal to

The number of real values of the triplet $(p, q, r)$ for which $p \operatorname{cos}^2 x+q \operatorname{sin}^2 x+r=0$ is satisfied by all real x , is