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

Question 30 Trigonometric Identities Exercise 18

(tan A + sin A)/ (tan A – sin A) = (sec A + 1)/ (sec A – 1)

In LHS, first convert tan A in terms of sin A and cos A

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\begin{aligned} &\text { L.H.S. }=\frac{\tan A+\sin A}{\tan A-\sin A}=\frac{\frac{\sin A}{\cos A}+\sin A}{\frac{\sin A}{\cos A}-\sin A}=\frac{\frac{\sin A+\sin A \cos A}{\cos A}}{\frac{\sin A-\sin A \cos A}{\cos A}}\\ &=\frac{\sin A(1+\cos A)}{\sin A(1-\cos A)}=\frac{1+\cos A}{1-\cos A}\\ &=\frac{\frac{1}{\cos \mathrm{A}}+1}{\frac{1}{\cos \mathrm{A}}-1}=\frac{\sec \mathrm{A}+1}{\sec \mathrm{A}-1}=\text { R.H.S. } \end{aligned}

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