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

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

Question 643554: Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2
Thank You.

Answer by lwsshak3(11628) (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

RELATED QUESTIONS
PROVE THAT tanx + cotx / secx + cosecx = 1 / sinx +... (answered by Alan3354)

prove that{{{ (secX-cosecX)/(secX+cosecX)}}}... (answered by Boreal)

Simplify [1/(tanx + cotx + secx + cosecx)]² (answered by Edwin McCravy)

Prove the identity. Show steps to prove it equals to secx cscx 1/cotx+1/tanx=secx... (answered by srinivas.g)

verify this identity tanx(cotx + tanx) =... (answered by lwsshak3)

prove the identity tanx/secx+1 =... (answered by MathLover1)

Prove that the ff equation is an identity: ((1 - tanX)/(secX)) + ((secX)/(tanX)) =... (answered by jim_thompson5910)

Prove: 1)sec^2x(1-sin^2x)=1 2)sinxcosxtanx=1-cos^2x 3)(cotx/cscx)=cosx... (answered by drk)

Verify the identity (secx-tanx)^2=... (answered by DrBeeee)