JIPMAT (QA) PYQs

Given below are two statement:

Statement I: If $\sin (\theta)=\frac{5}{13}$, then the value of $\tan (\theta)=\frac{5}{12}$

Statement II: if $\cot (\theta)=\frac{12}{5}$, then the value of $\sin (\theta)=\frac{5}{12}$

In the light of the above statements, choose the correct answer form the question below:

Which of the following trigonometric identities are true?

$\begin{aligned} & \sin ^2\left(41^{\circ}\right)+\sin ^2\left(49^{\circ}\right)=1 \\ & \sin ^2\left(60^{\circ}\right)-2 \tan \left(45^{\circ}\right)-\cos ^2\left(30^{\circ}\right)=-1 \\ & \sin ^2(\theta)+\frac{1}{1+\tan ^2(\theta)}=1 \end{aligned}$

If $\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 3$, then value of $\sin^4\theta - \cos^4\theta$ is