Posted by **Alycia** on Friday, November 2, 2012 at 7:27am.

I'm only aloud to manipulate one side of the problem and the end result has to match the other side of the equation

Problem 1. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 2. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 3. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

- Math -
**Reiny**, Friday, November 2, 2012 at 8:08am
I did the first one, after fixing your typo

http://www.jiskha.com/display.cgi?id=1351823844

- Math -
**Reiny**, Friday, November 2, 2012 at 8:19am
#2 does not work for x=30° so there is a typo, or it is not and identity.

#3

LS = (1+sinx)/cosx + cosx/(1+sinx)

using LCD of cosx(1+sinx)

= ( (1+sinx)(1+sinx) + cos^2 x)/(cosx(1+sinx) )

= 1 + 2sinx + sin^2 x + cos^2 x)/(cosx(1+sinx) )

= (2 + 2sinx)/(cosx(1+sinx))

= 2(1+sinx)/(cosx(1+sinx))

= 2/cosx

= 2secx

= RS

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