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# Prove the following identities, where the angles involved are acute angles for which the expressions are defined - CBSE Class 10 - Mathematics

#### 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 to Current)
Chapter 8: Introduction to Trigonometry
Ex.8.40 | 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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