How do you prove that $cot^2x * sec^2x = csc^2x$ ?

Question

8459 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-18T02:10:17

By definition, we have

Thus

$cot^2(x)sec^2(x) = (cos(x)/sin(x))^2(1/cos(x))^2$

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

$=1/sin^2(x)$

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

$=csc^2(x)$

How do you prove that cot^2x * sec^2x = csc^2xcot^2x * sec^2x = csc^2x?