Question

Find the value of the following expression:

sin 60° cos 30° + cos 60° sin 30°

Answer 1

Given: sin 60° cos 30° + cos 60° sin 30°

Step-wise calculation:

1. Use the sine addition identity:

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

Therefore, the expression equals sin (60° + 30°).

2. Evaluate: sin (90°) = 1.

Verification via exact values:

`sin 60^circ = sqrt(3)/2`

`cos30^circ = sqrt(3)/2`

`cos60^circ = 1/2`

`sin30^circ = 1/2`

So, `(sqrt(3)/2)(sqrt(3)/2) + (1/2)(1/2)`

= `3/4 + 1/4` 

= 1