Q15 of 113 Page 560

Prove that

(sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0


= (sin 3x + sin x) sin x + (cos 3x – cos x) cos x


= (2sincos) sin x + (-2sin sin) cosx


= (2sin2x cosx) sinx-(2sin2x sinx) cosx


= 0.


Using the formula,


sinA + sinB = 2sin cos


cosA - cosB = -2sinsin


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