sin^2A.tan^2A + cos^2A.cot^2A =tan^2A + cot^2A -1
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Step-by-step explanation:
LHS = sin^2A.tan^2A + cos^2A.cot^2A
= sin^2A.(sec^2A - 1)+cos^2A.(cosec^2A-1)
= sin^2A.(1/cos^2A - 1)+cos^2A.(1/sin^2A - 1)
= (sin^2A/cos^2A) - sin^2A +(cos^2A/sin^2A)
- cos^2A
= tan^2A - sin^2A + cot^2A - cos^2A
= tan^2A+ cot^2A -(sin^2A+cos^2A)
= tan^2A+ cot^2A - 1
= RHS
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