Tan^3 theta/1+tan^2 theta+cot^3 theta/1+cot^2 theta=sec theta cosec theta-2 sin theta cos theta
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Step-by-step explanation:
tan³/1+tan² + cot³/1+cot²
=tan³/sec² + cot³/cosec²
=tan³cos² + cot³sin²
=sin³/cos³. cos²+ cos³/sin³.sin²
=sin³/cos+cos³/sin
=sin⁴+cos⁴/sincos
=(sin²+cos²)²-2sin²cos²/sincos
=1-2sin²cos²/sincos
=seccosec-2sincos
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