CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Login
Create free account


      Forgot password?

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

  Is there an error in this question or solution?

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
Solution Prove the following identities, where the angles involved are acute angles for which the expressions are defined Concept: Trigonometric Identities.
S
View in app×