Solution In LHS after rationalising we can apply the identity sinsup2sup A cossup2supA 1 L H S Rationalising the denominator

Trigonometric Identities Exercise 18

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

Question 34 Trigonometric Identities Exercise 18

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

Answer:

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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