sin^ 2 A tan A+cos^ 2 A * cot A + 2sin A * cos A = tan A + cot A
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Answer:
LHS = RHS
Step-by-step explanation:
LHS = sin²A×tanA+cos²A×cotA+2×sinA×cosA
= sin³A/cosA+cos³A/sinA+2sinAcosA
= (sin⁴A+cos⁴A+2sin²Acos²A)/sinAcosA
= (sin²A+cos²A)²/sinAcosA
= 1²/sinAcosA
= 1/sinAcosA
= (sin²A+co²A)/sinAcosA
= sin²A/sinAcosA+co²A/sinAcosA
= sinA/cosA+cosA/sinA
= tanA+cotA = RHS
LHS = RHS
sin²A×tanA+cos²A×cotA+2×sinA×cosA = tanA+cotA
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