Question :
Evaluate :
(i) \(sin^2 63 + sin^2 27\over cos^2 17 + cos^2 73\)
(ii) sin 25 cos 65 + cos 25 sin 65
Solution :
(i) \(sin^2 63 + sin^2 27\over cos^2 17 + cos^2 73\) = \(sin^2 (90 – 27) + sin^2 27\over cos^2 17 + cos^2 (90 – 17)\)
= \(cos^2 27 + sin^2 27\over cos^2 17 + sin^2 17\) = 1
(ii) sin 25 cos 65 + cos 25 sin 65
= sin 25 cos(90 – 25) + cos 25 sin(90 – 25)
= sin 25 sin 25 + cos 25 cos 25
= \(sin^2 25 + cos^2 25\) = 1
