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Prove the following identities, where the angles involved are acute angles for which the expressions are defined - Mathematics

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Question

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

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

Solution

L.H.S 

`cos A/(1 + sin A) + (1 + sin A)/cos A `

`(cos^2A+(1+sinA)^2)/((1+sinA)(cosA))`

`= (cos^2A + 1+sin^2A + 2sinA)/((1+sinA)(cosA))`

`=(sin^2+cos^2A+1+2sinA)/((1+sinA)(cosA))`

`=(1+1+2sinA)/((1+sinA)(cosA)) = (2+2sinA)/((1+sinA)(cosA))`

`=(2(1+sinA))/((1+sinA)(cosA)) = 2/(cosA) = 2secA`

=R.H.S

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 8: Introduction to Trigonometry
Ex. 8.4 | Q: 5.02 | Page no. 193
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Solution Prove the following identities, where the angles involved are acute angles for which the expressions are defined Concept: Trigonometric Identities.
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