Question

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

Answer 1

`S = (1 - cos t)^2.(1 + cos t)^2 + 1/[(1 - cos t)(1 + cos t)`

Explanation:

#sin^4 t = sin^2 t.sin^2 t = (1 - cos ^2 t)(1 - cos^2 t) = #= (1 - cos t)(1 + cos t)(1 - cos t)(1 + cos t) =# #= (1 - cos t)^2.(1 + cos t)^2#

`csc^2 t = 1/(sin^2 t) = 1/[(1 - cos t)(1 + cos t)]`
Finally:
`S = (1 - cos t)^2.(1 + cos t)^2 + 1/[(1 - cos t)(1 + cos t)]`