Question

What is `sec^4theta` in terms of non-exponential trigonometric functions?

Answer 1

`=8/(3+4cos2theta+cos4theta)`

Explanation:

`sec^4theta=1/cos^4theta`

`=1/(1/2(1+cos2theta))^2`

`=1/(1/4(1+2cos2theta+cos^2 2theta)`

`=4/(1+2cos2theta+1/2(1+cos4theta))`

`=8/(3+4cos2theta+cos4theta)`