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Question
Without using trigonometric tables, prove that:
(sin 65° + cos 25°)(sin 65° − cos 25°) = 0
Solution
LHS = (sin 65° + cos 25°) (sin 65° − cos 25°)
= `sin^2 65^circ - cos^2 25^circ`
= `sin^2 (90^circ - 25^circ) - cos^2 25^circ`
= `cos^2 25^circ - cos^2 25^circ`
= 0
= RHS
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