Question

Express each one of the following in terms of trigonometric ratios of angles lying between
0° and 45°

Sin 59° + cos 56°

Answer 1

We have `sin (90^@ -  theta) = cos theta` and `cos(90^@ - theta) = sin theta` so

`sin 596@ + cos 56^@ = sin(90^@ - 31^@) + cos 90^@ (90^@ - 34^@)`

`= cos 31^@ + sin 34^@`

Thus the desired expression is `cos 31^@ + sin 34^@`