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)
tadaaaah

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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