Question

How do you simplify `sqrt(tan^2x-2tanxsinx+sin^2x)`?

Answer 1

Factorize the expression under the square root as a quadratic trinomial in tanxsinx. Then simplify from there.
(This phone don't allow me to write in math styles sorry I can't give steps and final answer)

Answer 2

This can be factored as a perfect square trinomial, or of the form `(a + b)^2 = a^2 + 2ab + b^2`.

`=sqrt((tanx - sinx)^2)`

`=|tanx - sinx|`

Hopefully this helps!