Question

Evaluate without using a trigonometric table:

`(cot 38°)/(tan 52°) + (sec 25°)/("cosec" 65°) − (3 tan 35°)/(cot 55°)`

Answer 1

Use co-function identities:

tan⁡(90° − θ) = cot⁡ θ, sin⁡(90° − θ) = cos⁡ θ.

`(cot38°)/(tan 52°) = (cot 38°)/tan(90° −  38°) = (cot 38°)/(cot38°)`

`(sec 25°)/("cosec" 65°) = (sec 25°)/("cosec"(90° −  25°)) = (sec 25°)/(sec 25°) = 1`

`(3 tan 35°)/("cot"  55°) = (3 tan 35°)/("tan"(90° −  55°)) = (3 tan 35°)/(tan 35°) = 3`

1 + 1 − 3 = −1