cotx+sinx/1+cosx=cscx?

Question

Verify The equation

Answer 1

The solution is really so long to right over here,
u will have to change every trignometric function to "sin" and "cos". e.g: cotx = cosx/sinx
And then u will have to simplify. Try it, it is really easy.

Answer 2

(cotx+sinx)/(1+cosx), Is this what you want?
= cscx(cosx+sin^2(x))/(1+cosx)
Unless sin^2(x) = 1, this identity is wrong.

Answer 3

take LHS

cotx + [sinx/(1+cosx)]

multiply second term with (1-cosx)/(1-cosx)

=>cotx + [(sinx)/(1+cosx)]*[(1-cosx)/1-cosx)]

=>cotx + [(sinx)(1 -cosx)/(1-cos^2x)]

=>cotx + [sinx(1-cosx)/sin^2x)]

=>cotx + (1-cosx)/sinx

=>(cosx/sinx) + ((1-cosx)/sinx)

=>(cosx + 1 - cosx)/sinx

=>1/sinx

=>cscx

LHS = RHS

Answer 4

cot 30 = sqrt(3)
sin30 =.5
cos 30 = .5sqrt(3)
csc 30 = 2
(sqrt(3) +.5)/(1+.5sqrt(3)) not equal 2
This counterexample shows your expression is not an identity.