Help please to simplify as far as possible? (1-cos^2x)(1+cot^2x)(1−cos2x)(1+cot2x)

1 Answer
Martin C.
Feb 26, 2018

11

Explanation:

sin^2(x)+cos^2(x)=1|-cos^2(x)sin2(x)+cos2(x)=1∣−cos2(x)
sin^2(x)=1-cos^2(x)sin2(x)=1−cos2(x)
cot^2(x)=cos^2(x)/sin^2(x)cot2(x)=cos2(x)sin2(x)
(1-cos^2(x))(1+cot^2(x))(1−cos2(x))(1+cot2(x))
=sin^2(x)(1+cot^2(x))=sin2(x)(1+cot2(x))
=sin^2(x)(1+cos^2(x)/sin^2(x))=sin2(x)(1+cos2(x)sin2(x))
=sin^2(x)+cancel(sin^2(x))*cos^2(x)/cancel(sin^2(x))
=sin^2(x)+cos^2(x)
=1

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