How do you prove 1 + 1/(tan^2x) = 1/(sin^2x)?

1 Answer
Dec 12, 2015

I tried changing tan into sin and cos:

Explanation:

You can change the tangent as:
tan(x)=sin(x)/cos(x) and write it as:
1+1/(sin^2(x)/cos^2(x))=1/sin^2(x)
rearranging the left side:
1+cos^2(x)/sin^2(x)=1/sin^2(x)
(sin^2(x)+cos^2(x))/sin^2(x)=1/sin^2(x)
but: sin^2(x)+cos^2(x)=1
so:
1/sin^2(x)=1/sin^2(x)