Posted by **Alycia** on Thursday, November 1, 2012 at 10:37pm.

Im really struggling with these proving identities problems can somebody please show me how to do these? I'm only aloud to manipulate one side of the equation and it has to equal the other side of the equation at the end

Problem 1. Sinx/(cotx+1) + cosx/(tanx+1) = 1/(sinx+cosx)

Problem 2. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 3. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 4. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

- Math -
**Steve**, Friday, November 2, 2012 at 1:50am
often it's easier to work with just sin and cos.

working just on the left side, we have

sin/(cot+1) + cos/(tan+1)

sin/(cos/sin+1) + cos/(sin/cos+1)

sin^2/(cos+sin) + cos^2(sin+cos)

(sin^2 + cos^1)/(sin+cos)

1/(sin+cos)

ta-daaaah

- Math -
**Reiny**, Friday, November 2, 2012 at 7:46am
2. I think you have a typo , it should have been

sinx + cosx + sinxtanx + cosxcotx = secx + cscx

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

using a LCD of sinxcosx

= (sin^2x cosx + sinxcos^2x) + sin^3 x + cos^3 x)/(sinxcos)

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

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

= cosx/(sinxcosx) + sinx/(sinxcosx)

= 1/sinx + 1/cosx

= cscx + secx

= RS

try the others, following Steve's suggestion of changing all into sines and cosines

- Math -
**Alycia**, Friday, November 2, 2012 at 8:13am
thank you so much

- Math -
**Loved Chilapu**, Tuesday, March 29, 2016 at 2:49am
Prove 1-(sinxtanx)/(1+secx)

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