Question

How do you express `sin^4theta+cot^2theta` in terms of non-exponential trigonometric functions?

Answer 1

`(1-2cos^2(x)+3cos^4(x)-cos^6(x))/(1-cos^2(x))`

Explanation:

Writing
`(1-cos^2(x))^2+cos^2(x)/(1-cos^2(x))`
and this is

`((1-cos^2(x))^3+cos^2(x))/(1-cos^2(x))`
Using that

`(a-b)^3=a^2-3a^2b+3ab^2-b^3`

`(1-2cos^2(x)+3cos^4(x)-cos(x)^6)/(1-cos^2(x))`