Question

If A = 30° and B = 60°, verify that

(i) sin (A + B) = sin A cos B + cos A sin B

(ii) cos (A + B) = cos A cos B- sin A sin B

Answer 1

(i) use  the formula,

sin 30° = \(\frac{1}{2}\), \(sin 60° = \frac{\sqrt{3}}{2}, \, sin 90° = 1, cos 30° = \frac{\sqrt3}{2}, cos 60° = \frac{1}{2} \)

Hence proved

(ii) use the formula,

= \(\frac{\sqrt3}{2} \times \frac{1}{2} - \frac{\sqrt3}{2} \times \frac{1}{2}\)

= 0