Question

Prove the following identity: (Sin A/1+cos A) + (1+cos A/sin A) = 2 cosec A

Answer 1

Answer:

Step-by-step explanation:

$\frac{sinA}{1+cosA}$ +$\frac{1+cosA}{sinA}$

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

Since sin²A+cos²A = 1

⇒$\frac{(1-cos^2A)+(1+cosA)(1+cosA)}{sinA(1+cosA)}$

=$\frac{(1+cosA)(1-cosA) + (1+cosA)(1+cosA)}{sinA(1+cosA)}$

=$\frac{(1+cosA)(1-cosA+1+cosA)}{sinA(1+cosA)} \\\\=\frac{2}{sinA}\\\\\\ =2 cosecA$

Hence proved

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