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verifing an identity algebraically

Mathematics
Tutor: None Selected Time limit: 0 Hours

csc^4x-2csc^2x+1=cot^4x

Apr 9th, 2015

csc^4(x)−2csc^2(x)+1=cot^4(x)

(1sin(x))^4−2(1sin(x))^2+1=(cos(x)sin(x))^4

=1(1−cos^2(x))^22(1−cos^2(x))+(1−cos^2(x))^2/(1−cos^2(x))^2

=(1−2(1−cos^2(x))+(1−cos^2(x))^2) / (1−cos^2(x))^2

=(1−2+2cos^2(x)+(1−cos^2(x))^2) / (sin^2(x))^2

=(−1+2cos^2(x)+1+cos^4(x)−2cos^2(x)) / sin^4(x)

=cos^4(x) / sin^4(x)

=cot^4(x)


Apr 9th, 2015

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