SOLUTION: tanx/secx-1 - sinx /1+cosx = 2 cotx

Question 658764: tanx/secx-1 - sinx /1+cosx = 2 cotx
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
tanx/secx-1 - sinx /1+cosx = 2 cotx
start with left side
tan/sec-1-sin/1+cos
(sin/cos)/[(1/cos)-1]-[sin/(1+cos)]
=(sin/cos)/[(1-cos)/cos]-[sin/(1+cos)]
=[(sin/(1-cos)]-[sin/(1+cos)]
LCD: (1-cos)(1+cos)
=[sin(1+cos)-sin(1-cos)]/(1-cos)(1+cos)
=[sin(1+cos)-sin(1-cos)]/(1-cos^2)
=[sin(1+cos)-sin(1-cos)]/(sin^2)
divide by sin
=[1+cos-1+cos)]/(sin)
=2cos/sin
=2 cotx
verified: left side=right side
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