Question

Evaluate sin 60° cos 30° + sin 30° cos 60°. What is the value of sin (60° + 30°). What can you conclude?

Answer 1

Take sin 60°.cos 30° + sin 30°.cos 60°

= \(\frac{4}{4}=1\)  ..........(1)

Now take sin (60° + 30°)

= sin 90° = 1 …….. (2) 

From equations (1) and (2), I conclude that 

sin (60°+30°) = sin 60° . cos 30° + sin 30° . cos 60°. 

i.e., sin (A + B) = sin A . cos B + cos A . sin B