Question

Prove that:
tan³A/1+tan²A + cot³A/1+cot²A=1-2sin²A. cos²A/sin A. cosA​

Answer 1

Step-by-step explanation:

LHS

tan³A/1+tan²A+cot³A/1+cot²A

=tan³A/sec²A+cot³A/cosec²A

=(sin³A/cos³A)×cos²A+(cos³A/sin³A) ×sin²A

=sin³A/cosA+cos³A/sinA

=sin⁴A+cos⁴A/sinAcosa

=(sin²A)²+(cos²A)²/sinAcosA

=(sin²A+cos²A)²-2sin²Acos²A/ sinAcosA

=1-2sin²Acos²A/sinAcosA

=RHS