cosec A cosec A 1 cosec A cosec A 1 2 secsup2sup A

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

Question 21 Trigonometric Identities Exercise 18

cosec A/ (cosec A – 1) + cosec A/ (cosec A + 1) = 2 sec² A

Answer:

$\frac{\operatorname{cosec} A}{\operatorname{cosec} A-1}+\frac{\operatorname{cosec} A}{\operatorname{cosec} A+1}$

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

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