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

Question 424507: How to solve the following:
Establish the identity
2secX = cosX/(1+sinX) + (1+sinX)/cosX
Answer by lwsshak3(11628) (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
RELATED QUESTIONS
verify the identity cosx/1+sinx + cosx/1-sin... (answered by Alan3354)

Cosx/1-sinx - sinx/cosx = 1/cosx Prove the... (answered by Alan3354)

Prove the identity: Cosx/1-sinx - sinx/cosx = 1/cosx (answered by Alan3354)

Verify the identity:... (answered by scott8148)

Prove the identity: (Cosx /1-sinx) - (cosx/1+sinx)... (answered by lwsshak3)

Prove the identity ; (Cosx / 1 -sinx) - ( cosx / 1 +sinx) = 2tanx (answered by Jc0110)

(Sinx+tanx)(sinx�1+cosx)=sinx�tanx prove the identity (answered by josgarithmetic,MathTherapy)

Prove that: Cosx/1-sinx + 1-sinx/cosx =... (answered by josgarithmetic,MathTherapy)

prove that... (answered by mananth)