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

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

If $x \operatorname{cosec} \theta+y \cot \theta=z$, then the value of $x \cot \theta+y \operatorname{cosec} \theta$

If $\sin x+\sin ^2 x=1, x \in\left(0, \frac{\pi}{2}\right)$, then

$
\begin{aligned}
& \left(\cos ^{12} x+\tan ^{12} x\right)+3\left(\cos ^{10} x+\tan ^{10} x+\cos ^8 x+\tan ^8 x\right) \\
& +\left(\cos ^6 x+\tan ^6 x\right) \text { is equal to }
\end{aligned}
$