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

Question 27 Trigonometric Identities Exercise 18

$cos A cot A/ (1 - sin A) = 1 + cosec A$

Answer:

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

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

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