Question

Evaluate the following:

cosec³ 30° cos 60° tan³ 45° sin² 90° sec² 45° cot 30°

Answer 1

cosec³ 30° cos 60° tan³ 45° sin² 90° sec² 45° cot 30°............(i)

By trigonometric ratios, we have

`cosec 30^@ = 2, cos 60^@ = 1/2, tan 45^@ = 1     sin 90^@ = 1  sec 45^@ = sqrt2   cot 30^@ = sqrt3`

By substituting above values in (i), we get

`[2]^3 . 1/2 . (1)^3 . (1)^2 (sqrt2). sqrt3`

`=> 8. 1/2 . 1. 2 . sqrt3 => 8sqrt3`