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Posted by on Sunday, January 8, 2012 at 9:48pm.

The question is:
Set up a 2 column proof to show that each of the equations is an identity. Transform the left side to become the right side.
a. (tan + cot)^2 = sec^2 + csc^2

I'm having trouble with this.

b. (cos + sin)/cos + (cos - sin)/sin = csc sec

I'm having trouble with this too.

  • Trig - , Sunday, January 8, 2012 at 10:16pm

    a)
    you will need two identities here:
    tan^2 x + 1 = sec^2 x , and
    cot^2 x + 1 = csc^2 x

    LS = tanx + cotx)^2
    = tan^2x + 2tanxcotx + cot^2x
    = sec^2x - 1 + 2 + csc^2x , because (tanx)(cotx) = 1
    = sec^2 x + csc^2 x
    = RS

    b) LS = (sinx(cosx + sinx) + cosx(cosx - sinx))/(sinxcosx)
    = (sinxcosx + sin^2x + cos^2x - sinxcosx)/(sinxcosx)
    = 1/sinxcosx
    = (1/sinx)(1/cosx)
    = cscx secx
    = RS

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