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Question
Without using trigonometric tables, prove that:
sin53° cos37° + cos53° sin37° = 1
Solution
LHS = sin 53° cos 37° +cos 53° sin 37°
= sin (90° - 37°) cos 37° + cos (90° - 37°) sin 37°
= cos 37° + cos 37° + sin 37° sin 37°
= cos2 37 + sin2 37
= 1
= RHS
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