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

Question 20 Trigonometric Identities Exercise 18

(1 + sin A)/ cos A + cos A/ (1 + sin A) = 2 sec A

Answer:

Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

\begin{aligned} &=\frac{(1+\sin A)(1+\sin A)+\cos ^{2} A}{\cos A(1+\sin A)} \\ &=\frac{1+\sin A+\sin A+\sin ^{2} A+\cos ^{2} A}{\cos A(1+\sin A)} \\ &=\frac{1+2 \sin A+1}{\cos A(1+\sin A)}=\frac{2+2 \sin A}{\cos A(1+\sin A)} \\ &=\frac{2(1+\sin A)}{\cos A(1+\sin A)}=\frac{2}{\cos A}=2 \sec A \\ &=\text { R.H.S. } \end{aligned}

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