Question

Solve:cos^2 pi/5+ sin^24pi/5 Trigonometric fuctions:class 11

Answer 1

SOLUTION :

$cos {}^{2} ( \frac{\pi}{5} ) + sin {}^{2} (\frac{4\pi}{5}) \\ \\ = cos {}^{2} 36 + sin {}^{2} 144 \\ \\ = cos {}^{2} 36 + sin {}^{2} (180 - 36) \\ \\ = cos {}^{2} 36 \: + sin {}^{2} 36 = 1$

IDENTITIES USED :

$i) \: sin {}^{2} \alpha + cos {}^{2} \alpha = 1 \\ \\ ii)sin(180 - \alpha ) = sin \alpha$

[ NOTE : THE VALUE OF π IS TAKEN AS 180 TO SOLVE THIS QUESTION ]