How do you prove $Sin^2-cos^2=2sin^2-1$ ?

Question

17242 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-29T17:48:13

Replace in the equation $cos^2 x$ by $(1 - sin^2 x)$

We know this is true through manipulation of the Pythagorean identity:

$sin^2x+cos^2x=1" "=>" "cos^2x=1-sin^2x$

$sin^2 x - (1 - sin^2 x) = 2sin^2 x - 1.$

How do you prove Sin^2-cos^2=2sin^2-1Sin^2-cos^2=2sin^2-1 ?