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September 2, 2014

September 2, 2014

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

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 -
**Reiny**, Sunday, January 8, 2012 at 10:16pma)

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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