Prove that:(i) cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A(ii) cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A(iii) sin A + sin 2A + sin 4A + sin 5A = 4 cos A2 cos 3A2 sin 3A(iv) sin 3A + sin 2A − sin A = 4 sin A cos A2 cos 3A2(v) cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −34(vi) sinx2sin7x2+sin3x2sin11x2= sin 2x sin 5x.(vii) cos x cos x2-cos 3x cos9x2=sin 7x sin 8x

Prove that:(i) cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A co

1.	Prove that:(i) cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A(ii) cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A(iii) sin A + sin 2A + sin 4A + sin 5A = 4 cos A2 cos 3A2 sin 3A(iv) sin 3A + sin 2A − sin A = 4 sin A cos A2 cos 3A2(v) cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −34(vi) sinx2sin7x2+sin3x2sin11x2= sin 2x sin 5x.(vii) cos x cos x2-cos 3x cos9x2=sin 7x sin 8x
Answer» Prove that: (i) cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A (ii) cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A (iii) sin A + sin 2A + sin 4A + sin 5A = 4 cos $\frac{A}{2}$ cos $\frac{3 A}{2}$ sin 3A (iv) sin 3A + sin 2A − sin A = 4 sin A cos $\frac{A}{2}$ cos $\frac{3 A}{2}$ (v) cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = − $\frac{3}{4}$ (vi) $\sin \frac{x}{2} \sin \frac{7 x}{2} + \sin \frac{3 x}{2} \sin \frac{11 x}{2} = \sin 2 x \sin 5 x .$ (vii) $\cos x \cos \frac{x}{2} - \cos 3 x \cos \frac{9 x}{2} = \sin 7 x \sin 8 x$