Question

Evaluate sin² 73 + sin² 17 divided by cos² 37 + cos² 53

Answer 1

$cos {}^{2} (90 - 73) + sin {}^{2} 17 \div sin {}^{2} (90 - 37) + cos {}^{2} 53 \\ \\ cos {}^{2}17 + sin {}^{2} 17 \div sin {}^{2}53 + cos {}^{2}53 \\ \\ 1 \div 1 \\ \\ 1$

Answer 2

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\: Given:-\:\:\:\:}}$

$\sf \hookrightarrow \dfrac{sin{}^{2}73{}^{\circ}+sin{}^{2}17{}^{\circ}}{cos{}^{2}37{}^{\circ}+cos{}^{2}53{}^{\circ}}$

$\sf {\purple{Formula\:used}}\\ \\ \sf \longrightarrow sin(90{}^{\circ}-\theta)=cos\theta$

Now

$\sf\underline{\purple{\:\:\: Solution:-\:\:\:\:}}$

$\sf:\implies \dfrac{sin{}^{2}73{}^{\circ}+sin{}^{2}(90{}^{\circ}+73{}^{\circ})}{cos{}^{2}37{}^{\circ}+cos{}^{2}(90{}^{\circ}-37{}^{\circ})}\\ \\ \sf:\implies\dfrac{ sin{}^{2}73{}^{\circ}+cos{}^{2}73{}^{\circ}}{cos{}^{2}37{}^{\circ}+sin{}^{2}37{}^{\circ}}\\ \\ \sf\:\::\Longrightarrow sin{}^{2}\theta+cos{}^{2}\theta=1\\ \\ \sf:\implies \dfrac{1+1}{1+1}\\ \\ \sf:\implies\cancel{ \dfrac{2}{2}}=1$

$\boxed{\sf{\fbox{\dfrac{sin{}^{2}73{}^{\circ}+sin{}^{2}17{}^{\circ}}{cos{}^{2}37{}^{\circ}+cos{}^{2}53{}^{\circ}}=1}}}$