Question

prove that 1 + 1/tan^2x = 1/sin^2x

Answer 1

\[\begin{align} 1+{1 \over \tan^2(x)} &={1 \over \sin^2(x)}\\{\sin^2(x) \over \sin^2(x)}+{\cos^2(x) \over \sin^2(x)} &={1 \over \sin^2(x)} \\ {\sin^2(x)+cos^2(x) \over \sin^2(x)}&={1 \over \sin^2(x)} \\
{1 \over \sin^2(x)}&={1 \over \sin^2(x)}
\end{align}\]So we're done.

Answer 2

rewrite 1/tan^2x as cos^2x/sin^2x.

rewrite 1 as sin^2x/sin^2x so that you have a common denominator.

add.

sin^2x + cos^2x=1. so both sides of the equation should look the same.

Answer 3

thankss!

Answer 4

You're welcome.