prove that tan A - cot A /sin A cos A = tan^2-cot^2A
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Step-by-step explanation:
LHS
(tanA-cotA)/sinAcosA
=(sinA/cosA - cosA /sinA)/sinAcosA
= (sin^2A-cos^2A/sinAcosA)/sinAcosA
=(sin^2A-cos^2A)sin^2Acos^2A
=sin^2A/sin^2Acos^2A -cos^2A/sin^2Acos^A
=1/cos^2A - 1/sin^2A
=sec^2A- cosec^2A
= (1+tan^2A)-(1+cot^2A)
=tan^2A-cot^2A = RHS
Hence proved the result
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