Prove the following trigonometric identities:
tanA/(1+tan²A)²+cot²A/(1+cot²A)²=sinAcosA
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tanA / (1+tan²A)² + cotA / (1+cot² A)² = sinA .cosA proved
Step-by-step explanation:
To prove: tanA /(1+tan²A)² +cotA / (1+cot²A)² = sinA .cosA
Proof:
We know Sec²θ = 1 + Tan²θ and Cosec²θ = 1 + Cot²θ
LHS = tanA /(1+tan²A)² + cotA/(1+cot²A)²
= tan A / (Sec²A)² + cotA / (Cosec²θ)²
= SinA/CosA / 1/(Cos²A)² + CosA/SinA / 1/(Sin²A)²
= SinA.CosA.cos²A + CosA.SinA.Sin²A
= SinA.CosA (Sin²A + Cos²A)
= SinA.CosA
= RHS
RHS = LHS
Hence proved.
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