Question

How do you simplify with trigo identities `(sinx)/(2tanxsec^2x)` so it can result `1/2cos^3x` ?

Answer 1

Please see below.

Explanation:

Let's substitute for `tanx` and `sec^2x` in terms of `cosx`:

`tanx=sinx/cosx`

`secx=1/cosx`

`sinx/(2sinx/cosx(1/cos^2x))=sinx/((2sinx)/cos^3x)=(sinxcos^3x)/(2sinx)=(cancelcolor(red)sinxcos^3x)/(2cancelcolor(red)sinx)=1/2cos^3x`