Question

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

 sin 67° + cos 75°

Answer 1

We know that `sin(90^@ - theta) = cos theta` and `cos(90^@ - theta) = sin theta` So

`sin 67^@ + cos 75^@ = sin(90^@ - 23^@) + cos(90^@ - 15^@)`

`= cos 23^@ + sin 15^@`

Thus the desired expression is `cos 23^@ + sin 15^@`