Question

solve it fast........................

Answer 1

LHS= tan³A/1+tan²A +cot³A/1+cot²A
=(sin³A/cos³A)/(1+sin²A/cos²A)+(cos³A/sin³A)/(1+cos²A/sin²A)
=(sin³A/cos³A)/(cos²A+sin²A/cos²A)+(cos³A/sin³A)(sin²A+cos²A/sin²A)
=(sin³A/cos³A)/(1+cos²A)+ (cos³A/sin³A)/(1+sin²A)
=sin³A/cosA + cos³A/sinA
=(sin⁴A+cos⁴A)/sinAcosA
=(sin²A)²+(cos²A)²/sinAcosA
=(sin²A+cos²A)²-2sin²Acos²A/sinAcosA
=1-2sin²Acos²A/sinAcosA
=1/sinAcosA - 2sin²Acos²A/sinAcosA
=cosecAsecA-2sinAcosA
RHS(HENCE PROVED)