How do you verify $sin^2 (-x) / tan^2 x = cos^2 x$ ?

Question

15494 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-16T22:05:10

We will be using the following:

Then, when $cos(x)!=0$ and $sin(x)!=0$ , we have

$sin^2(-x)/tan^2(x) = (sin(-x))^2/(sin(x)/cos(x))^2$

$=(-sin(x))^2/(sin^2(x)/cos^2(x))$

$=sin^2(x)/(sin^2(x)/cos^2(x))$

$=1/(1/cos^2(x))$

$=cos^2(x)$

How do you verify sin^2 (-x) / tan^2 x = cos^2 xsin^2 (-x) / tan^2 x = cos^2 x?