SOLUTION: Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2 Thank You.

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Question 643554: Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2
Thank You.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2
Identities:
tan^2+1=sec^2
cot^2+1=csc^2
..
Start with left side:
(1-tanx)^2+(1- cotx)^2
=(1-2tanx+tan^2x)+(1-2cotx+cot^2x)
=sec^2x+csc^2x-2(tanx+cotx)
=sec^2x+csc^2x-2(sinx/cosx+cosx/sinx)
=sec^2x+csc^2x-2[(sin^2x+cos^2x)/(cosx*sinx)]
=sec^2x+csc^2x-2[1/(cosx*sinx)]
=sec^2x+csc^2x-2[(1/cosx)*(1/sinx)]
=sec^2x+csc^2x-2secx*cscx
=(secx-cscx)^2
left side=right side
given identities are equivalent