Question

Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`

Answer 1

`(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`

tan(49°) = cot(41°)

(because 49° + 41° = 90°)

`(cot^2 41°)/(tan^2 49°) = (cot^2 41°)/(cot41°)^2 = 1`

`(sin^2 75°)/(cos^2 15°)`

sin75° = cos15°

`(sin^2 75°)/(cos^2 15°) = (cos15°)^2/(cos15°)^2 = 1`

1 − 2(1) = 1 − 2

= −1