Prove that:
tan³A/1+tan²A + cot³A/1+cot²A=1-2sin²A. cos²A/sin A. cosA
Answers
Answered by
4
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
Similar questions