JIPMAT (QA) PYQs

In $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{BC}=5 \ \mathrm{cm}, \mathrm{AC}-\mathrm{AB}=1 \mathrm{~cm}$, then $\frac{1+\sin (\mathrm{C})}{1+\cos (\mathrm{C})}$ is

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?

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