Question

Evaluate the following and justify your answer
$\frac{{\sin }^2{15}^o+{\sin }^2{75}^o}{{\cos }^2{36}^o+{\cos }^2{54}^o}$

Answer 1

$\frac{si{n}^2{15}^{\circ }+si{n}^2{75}^{\circ }}{co{s}^2{36}^{\circ }+co{s}^2{54}^{\circ }}$

$\Rightarrow sin(90-\theta )=cos\theta$ & $si{n}^2\theta +co{s}^2\theta =1$ & $cos(90-\theta )=sin\theta$

$\Rightarrow \frac{si{n}^2(90-75)+si{n}^2{75}^{\circ }}{co{s}^2(90-54)+co{s}^{2}54}$

$\Rightarrow \frac{co{s}^{2}75+si{n}^{2}75}{si{n}^{2}54+co{s}^{2}54}=\frac{1}{1}=1$