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

1 Answer
Rafael
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)#

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