SOLUTION: prove step-by-step that: (secx-1/tanx) + (tanx/secx+1) = (2sinx/1+cosx) This is really important, any help ASAP would be awesome, thank you!!

Question 569738: prove step-by-step that:
(secx-1/tanx) + (tanx/secx+1) = (2sinx/1+cosx)
This is really important, any help ASAP would be awesome, thank you!!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
prove step-by-step that:
(secx-1/tanx) + (tanx/secx+1) = (2sinx/1+cosx)
start with left side
(secx-1/tanx) + (tanx/secx+1)
add terms
[(secx-1)(secx+1)+tanx*tanx]/tanx(secx+1)
=[(sec^2x-1)+tan^2x]/tanx(secx+1)
=[tan^2x+tan^2x]/tanx(1/cosx+1)
=2tan^2x/tanx(1+cosx)/(cosx)
=2tanx/(1+cosx)/(cosx)
=2tanxcosx/1+cosx
=2(sinx/cosx)*cosx/(1+cosx)
=2sinx/(1+cosx)
verified: left side=right side
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