How do you prove sec^4(x)-csc^2(x)=tan^2(x)-cot^2(x)?

1 Answer
Oct 25, 2015

See explanation.

Explanation:

Are you sure you didn't mean sec^2x-csc^2x=tan^2x-cot^2x? I don't think the data you provided is an identity. Anyway, if you meant sec^2x, here it is:

[1]" "sec^2x-csc^2x

Pythagorean Identity: sec^2alpha=1+tan^2alpha

[2]" "-=(1+tan^2x)-csc^2x

Pythagorean Identity: csc^2alpha=1+cot^2alpha

[3]" "-=(1+tan^2x)-(1+cot^2x)

[4]" "=1+tan^2x-1-cot^2x

[5]" "=tan^2x-cot^2x

color(blue)( :.sec^2x-csc^2x=tan^2x-cot^2x)