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Question -

Prove that: cos 7π/12 + cos π/12 = sin 5π/12 – sin π/12



Answer -

We know that, 7π/12 = 105°, π/12 = 15°; 5π/12 = 75°
Let us consider LHS: cos 105° + cos 15°
cos (90° + 15°) + sin (90° – 75°)
-sin 15° + sin 75°
sin 75° – sin 15°
= RHS
∴ LHS = RHS
Hence proved.

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