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Question
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
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Solution
To Prove: `((1 + tan^2 A))/((1 + cot^2 A))` = sec2 A – 1
LHS.
We have, `(((1 + sin^2 A)/(cos^2 A)))/(((1 + cos^2 A)/(sin^2 A)))`
= `[(((cos^2 A + sin^2 A))/(cos^2 A))/(((sin^2 A + cos^2 A))/(sin^2 A))]`
= `((1/cos^2 A))/((1/sin^2 A))` ...[As sin2 A + cos2 A = 1]
= `((sin^2 A))/((cos^2 A))`
= tan2 A
= sec2 A – 1
Hence, proved.
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