Question

How do you find the exact functional value sin(60˚+45˚) using the cosine sum or difference identity?

Answer 1

`sin (60^@ + 45^@) = (sqrt(3) + 1)/(2sqrt(2))`

Explanation:

Using the sine identity:
`sin (A +- B) = sin A cos B +- cos A sin B`

`sin (60^@ + 45^@) = sin 60^@ cos 45^@ + cos 60^@ sin 45^@`
`= sqrt(3)/2 xx 1/sqrt(2) + 1/2 xx 1/sqrt(2) = (sqrt(3) + 1)/(2sqrt(2))`

If you want to use the cosine identity:
`cos (A +- B) = cos A cos B ""_+^(-) sin A sin B`

`sin A = cos (A-90^@)`

`sin (60^@+45^@) = cos (60^@ - 45^@)`
`= cos 60^@ cos 45^@ + sin 60^@ sin 45^@`
`= 1/2 xx 1/sqrt(2) + sqrt(3)/2 xx 1/sqrt(2)`
`= (sqrt(3) + 1)/(2sqrt(2))`