Question

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

cot 85° + cos 75°

Answer 1

We know that `cot (90^@ - theta) = tan theta` and `cos (90^@ - theta) = sin theta` so

`cot 85° + cos 75° = cot(90^@ - 5^@) + cos(90^@ - 15^@)`

`= tan 5^@ + sin 15^@`

Thus the desired expression is `tan 5^@ + sin 15^@`