SOLUTION: How to solve the following: Establish the identity 2secX = cosX/(1+sinX) + (1+sinX)/cosX

Algebra ->  Trigonometry-basics -> SOLUTION: How to solve the following: Establish the identity 2secX = cosX/(1+sinX) + (1+sinX)/cosX      Log On


   

Question 424507: How to solve the following:
Establish the identity
2secX = cosX/(1+sinX) + (1+sinX)/cosX
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How to solve the following:
Establish the identity
2secX = cosX/(1+sinX) + (1+sinX)/cosX
..
Starting from the right side,
cosX/(1+sinX)+(1+sinX)/cosX
add the two fractions using LCD, cosx(1+sinx)
=cos^2x+(1+sinx)^2/cosx(1+sinx)
=cos^2x+1+2sinx+sin^2x/cosx(1+sinx)
cos^2x+sin^2x=1
=2+2sinx/cosx(1+sinx)
=2(1+sinx)/cosx(1+sinx)
=2/cosx
=2secx
Identity established: right side=left side