1.

Prove that (sin 65° + cos 25°)(sin 65° − cos 25°) = 0.

Answer»

(sin 65° + cos 25°)(sin 65° − cos 25°) = 0

LHS = (sin 65° + cos 25°)(sin 65° − cos 25°)

= sin2 65° – cos2 25°

= sin2 65° – cos2 (90 – 65)°

= sin2 65° – sin2 65°

= 0

= RHS



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