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

Question 22 Trigonometric Identities Exercise 18

cot A – tan A = (2cos2 A – 1)/ (sin A – cos A)

Answer:

Firstly, we need to convert cot A and tan A in terms of sin A and cos A .

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

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