Question

I need help doing step 1 of this problem?

Answer 1

`\sin(2x)=\cfrac{2\tan(x)}{1+\tan^2(x)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2\tan(x)}{1+\tan^2(x)}\implies \cfrac{2\tan(x)}{\sec^2(x)}\implies \cfrac{2\tan(x)}{~~ ( 1 )/( \cos^2(x) ) ~~}\implies 2\tan(x)\cos^2(x) \\\\\\ \cfrac{2\sin(x)}{\cos(x)}\cdot \cos^2(x)\implies 2\sin(x)\cos(x)\implies \sin(2x)`

Answer 2

`sec^(2) x\\`

Explanation:

1 +
`tan^(2) x` =
`sec^(2) x\\`

Pythagorean identity

:D