JIPMAT 2021 (QA) PYQs

If $\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}$, then $(\sin \theta-\cos \theta)$ is equal to :

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 $\sin (θ) - \cos (θ) = 0$, the value of sin⁴ (θ) + cos⁴ (θ) is: