(Q21)Evaluate sin 60° cos 30° + sin 30° cos 60°. What is the value of sin (60° + 30°). What can you conclude?

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

=
√
2
.
√
2
 +
1
.
1
=
(√)2
4
 +
1
=
4
 +
1
=
+ 1
=
= ............(1)

Now take sin (60° + 30°)

= sin ° = ..........(2)

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

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

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