# ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities

Question 34 Trigonometric Identities Exercise 18

\sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{\sin A}{1+\cos A}

Solution:

In LHS after rationalising, we can apply the identity sin2 A + cos2A =1

L. H. S. = \sqrt{\frac{1-\cos A}{1+\cos A}}

Rationalising the denominator

\begin{aligned} &=\sqrt{\frac{(1-\cos A)(1-\cos A)}{(1+\cos A)(1-\cos A)}} \\ &=\sqrt{\frac{(1-\cos A)^{2}}{1-\cos ^{2} A}}=\sqrt{\frac{(1-\cos A)^{2}}{\sin ^{2} A}} \\ &=\frac{1-\cos A}{\sin A}=\frac{1}{\sin A}-\frac{\cos A}{\sin A} \\ &=\operatorname{cosec} A-\cot A=\text { R.H.S. } \end{aligned}

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