Question

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

Answer 1

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

Answer 2

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

Answer 3

thank you so much

Answer 4

Prove 1-(sinxtanx)/(1+secx)