tanA/(1 +tan^A)^+cotA/(1+cotA^)^=sinA*cosA
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Answer:
Step-by-step explanation:
Solution:
L.H.S. = tanA/(1+tan²A)² + cotA/(1+cot²A)²
= tanA/(sec²A)² + cotA/(cosec²A)²
= tanA/sec⁴A + cotA/cosec⁴A
= (sinA/cosA ÷ 1/cos⁴A) + (cosA/sinA ÷ 1/sin⁴A)
= sinA×cos³A + cosA×sin³A
= sinA×cosA(cos²A+sin²A)
= sinA × cos A
= RHS
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