Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections $A$ and $B$. Tower is supported by wires from a point $O$. Distance between the base of the tower and point $O$ is $36 cm$. From point $O,$ the angle of elevation of the top of the section $B$ is $30°$ and the angle of elevation of the top of the section $A$ is $45°$.

Based on the above information, answer the following question.

Find the area of $△OPB$.

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections $A$ and $B$. Tower is supported by wires from a point $O$. Distance between the base of the tower and point $O$ is $36 cm$. From point $O,$ the angle of elevation of the top of the section $B$ is $30°$ and the angle of elevation of the top of the section $A$ is $45°$.

Based on the above information, answer the following question.

Find the height of the section $A$ from the base of the tower.

$\left({\cos }^{4}A-{\sin }^{4}A\right)$ on simplification, gives

If $\sin \theta +\cos \theta =p$ and $sec\theta +\cos ec\theta =q$, then prove that $q\left(p^2-1\right)=2p$.

If $\tan \theta =\frac{x}{y}$, then $\cos \theta$ is equal to 

Prove that $\left(\sin \theta +\cos \theta \right)\left(\tan \theta +\mathrm{co}t \theta \right)=sec \theta +\cos ec \theta$.