Derive the formula for
sin 2xand cos3x and hence evaluate sin 18° .
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Step-by-step explanation:
1) sin (A + B) = sin A cos B + cos A sin B
sin (x + x) = sin x cos x + cos x sin x
=> sin 2x = 2 sin x cos x
2) cos (A + B) = cos A cos B - sin A sin B
cos (2x + x) = cos 2x cos x - sin 2x sin x
=> cos 3x = (2 cos²x - 1) cos x - 2 sin x cos x sin x
=> 2 cos³x - cos x - 2 sin²x cos x
=> 2 cos³x - cos x - 2 [ 1-cos²x] cos x
=> 2 cos³x - cos x - 2 cos x + 2 cos³x
=> 4 cos³x - 3 cos x
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