Question

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

cosec 54° + sin 72°

Answer 1

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

`cosec 54° + sin 72° = cosec(90^@ - 36^@) + sin (90^@ - 18^@)`

`= sec 36^@ + cos 18^@`

Thus the desired expression is `sec 36^@ + cos 18^@`