Posted by Alycia on .
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,
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,
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,
thank you so much

Math 
Loved Chilapu,
Prove 1(sinxtanx)/(1+secx)