Question

Prove ${\sin }^2\theta +{\cos }^2\theta =1$

Answer 1

$\sin \theta =\frac{\text{Opposite side to}\theta }{\text{Hypotenuse}}$

$\cos \theta =\frac{\text{Adjacent side to}\theta }{\text{Hypotenuse}}$

${\sin }^2\theta =\frac{(\text{Opposite side to}\theta {)}^2}{({\text{Hypotenuse )}}^2}$

${\cos }^2\theta =\frac{\text{(Adjacent side to}\theta {)}^2}{{\text{(Hypotenuse )}}^2}$

${\sin }^2\theta +{\cos }^2\theta$

$\frac{(\text{Opposite side to}\theta {)}^2}{({\text{Hypotenuse )}}^2}+$$\frac{\text{(Adjacent side to}\theta {)}^2}{{\text{(Hypotenuse )}}^2}$

$\frac{{\text{Hypotenuse}}^2}{{\text{Htpotenuse}}^2}=1$