Can anyone prove this?

Tom Carrick asked Jun 3, 2023

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34 votes

Tom Carrick asked Jun 3, 2023

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16 votes

Answer:

Rewrite
csc^4x-cot^4x by applying exponent rule
a^(bc)=(a^b)^c :

$\implies (csc^2x)^2-(cot^2x)^2$

Apply difference of two squares formula
x^2-y^2=(x+y)(x-y) :

$\implies (csc^2x+cot^2x)(csc^2x-cot^2x)$

Using trig identity
$1+cot^2x=csc^2x \implies 1=csc^2x-cot^2x$

$\implies (csc^2x+cot^2x)(1)$

$\implies csc^2x+cot^2x$

Snroki answered Jun 10, 2023

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