Evaluate :

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

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