Please prove this trigonometric identity
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Step-by-step explanation:
tan³A/1+tan²A+cot³A/1+cot²A
=tan³/sec²A+cot³A/cosec²A
=sin³A/cosA+cos³A/sinA
=sin⁴A+cos⁴A/sinAcosA
=(sin²A+cos²A)²-2sin²Acos²A/sinAcosA
=1-2sin²Acos²A/sinAcosA
=1/sinAcosA-2sin²Acos²A/sinAcosA
=secAcosecA-2sinAcosA
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