Question

Evaluate the following in the simplest form:

sin 60° cos 30° + cos 60° sin 30°

Evaluate the following:

sin 60° cos 30° + cos 60° sin 30°

Answer 1

sin 60° cos 30° + cos 60° sin 30°

= `\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}+\frac{1}{2}\times\frac{1}{2}`

= `\frac{3}{4}+\frac{1}{4}`

= 1

Answer 2

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

By trigonometric ratios we have,

`sin 60° = sqrt3/2  sin 30°`

= `1/2`

`cos 30° = sqrt3/2  cos 60°`

= `1/2`

Substituting above values in (i), we get

`sqrt3/2 . sqrt3/2 + 1/2 . 1/2`

= `3/4 + 1/4`

= `4/4`

= 1