Question

2 sin2 5 degree +sin2 10 degree+ sin2 15 degree+................+ sin2 85 degree=????????

explain

Answer 1

#ANSWER #

sin^2 5 + sin^2 10 + sin^2 15 + ..... + sin^2 85

= cos^2 (90 – 5) + cos^2 (90 – 10) + ..... cos^2 (90 – 45) +sin^2 50+ ..... + sin^2 80 + sin^2 85

= cos^2 85 + cos^2 80 ..... + cos^2 45 + .....+ sin^280 + sin^2 85

= (sin^2 85 + cos^2 85) + (sin^2 80 + cos^2 80) +........ + cos^2 45 

$= 1 + 1 + .......... + ( { \frac{1}{ \sqrt{2} }) }^{2} \\ = 8 + \frac{1}{2} = \frac{17}{2} = 9.5$
$\: THANX$