Question

prove that (cotA-1)^2+(cotA+1)^2=2cosec^2A

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Answer 1

Explanation:

L.H.S.

=(cotA-1)²+(cotA+1)²

=cot²A-2.cotA.1+1²+cot²A+2.cotA.1+1²

=cot²A-2cotA+1+cot²A+2cotA+1

=cot²A+cot²A+1+1

=2+2cot²A

=2(1+cot²A)

=2(1+cos²A/sin²A)

=2(sin²A+cos²A/sin²A)

=2×1/sin²A

=2cosec²A= R.H.S

#Proved.

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