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If lies in the first quadrant And cos x = 8/17, then prove that
Given x lies in the first quadrant i.e. 0 < x < π/2 And cos x = 8/17
We know that
LHS
= cos(30 + x) + cos(45 – x) + cos(120 – x)
We know that cos(A ±B) = cosA cosB ∓ sinA sinB
= cos 30° cos x – sin 30° sin x + cos 45° cos x + sin 45° sin x + cos 120° cos x + sin 120° sin x
= cos x(cos 30° + cos 45° + cos 120°) + sin x(-sin 30° + sin 45° + sin 120°)
= RHS
Hence, proved.
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