Question

State true or false:

${\sin }^{2}A+{\cos }^{2}A=1$

Answer 1

${\sin }^{2}A+{\cos }^{2}A=1$. Its a standard identity.

We know that $\sin A=\frac{P}{H}$ and $\cos A=\frac{B}{H}$

Hence ${\sin }^{2}A=\frac{P^2}{H^2}$ and $co{s}^{2}A=\frac{B^2}{H^2}$

Hence adding the above given functions $si{n}^{2}A+co{s}^{2}A$ we get

$si{n}^{2}A+co{s}^{2}A=\frac{H^2}{H^2}=1$

Using $P^2+B^2=H^2$ by Pythagoras Theorem