Question 57

$$[\frac{SinA}{(1+CosA)}]+[\frac{(1+CosA)}{SinA}]$$ is equal to

Solution

Expression : $$[\frac{SinA}{(1+CosA)}]+[\frac{(1+CosA)}{SinA}]$$

Taking L.C.M, we get :

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

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

Using $$(sin^2 A + cos^2 A = 1)$$

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

= $$\frac{2}{sin A} = 2 cosec A$$

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