Establish the identity CSC4 x cot4 x CSC2 x cot2 xSolutio

Establish the identity. CSC^4 x - cot4 x = CSC^2 x + cot^2 x

Solution

csc⁴x-cot⁴x=csc²x+cot²x

starting with left side

csc⁴x-cot⁴x

(csc²x)²-(cot²x)²

(csc²x -cot²x)(csc²x+ cot²x)

And csc²x-cot²x=1

1(csc²x+cot²x)=csc²x+ cot²x that is the right side