Simplify the expression tan4 9 tan2 912 Express your answe

Simplify the expression tan4 /(9 tan^2() + 9)^1/2 . Express your answer in terms of sines and/or cosines. Assume is in quadrant I.

Solution

tan⁴/(9 tan^2() + 9)^1/2

= tan⁴/[9(tan^2() + 1)]^1/2

= tan⁴/[9*sec^2()]^1/2

= tan⁴/(3*sec)

= (sin⁴/cos⁴)/(3/cos) = (sin⁴/3cos³)