Question

Prove that ,1+cosA - sin^2A /sinA(1+cosA) =cotA

Answer 1

Proof

$\Longrightarrow{\mathsf{\frac{1 + cosA - {sin}^{2}A }{sinA(1 + cosA)}}} \\ \\ \Longrightarrow{\mathsf{\frac{(1 - {sin}^{2}A) + cosA }{sinA(1 + {cos}^{2}A)}}} \\ \\ \Longrightarrow{\mathsf{\frac{ {cos}^{2} A + cosA}{sinA(1 + cosA)}}} \\ \\ \Longrightarrow{\mathsf{\frac{cosA(1 + cosA)}{sinA(1 + cosA)}}} \\ \\ \Longrightarrow{\mathsf{\frac{cosA}{sinA} = cotA}}$

Identities Used

• cot∅/sin∅ = cot∅
• 1 - sin²∅ = cos²∅

Hence Proved

Answer 2

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