1.

Express each of the following as the product of two trigonometric reactions. (i) sin 12x + sin 4x (ii) sin 7A – sin 3A (iii) cos 2θ + cos 6θ (iv) sin 80° – sin 40°

Answer»

(i) sin12x + sin4x = 2.sin \(\frac{12x + 4x}{2}.cos\frac{12x - 4x}{2}\). cos 

(ii) sin7A – sin3A = 2cos5A.sin2A 

(iii) cos6θ + cos2θ = 2 cos4θ.cos2θ 

(iv) sin 80° – sin 40° = 2 cos60°. sin 20° = 2. sin 20° = sin 20°



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