Question

Prove
(1+Cosx)/sinx = sinx /( 1-cosx)

1st what do i need to take note??

Answer 1

Do you want to add any brackets? So far, it says this:
\[1 + \frac{\cos x}{\sin x} = \frac{\sin x}{1} - \cos x\]

Answer 2

Thanks for editing the post and adding the brackets...

Answer 3

note: multiply top and bottom by \(1-\cos x\) and note the pythagorean identity.

Answer 4

First thing: multiply both sides by certain values to remove the fractions. Eg:
\[\frac{a}{b} = \frac{c}{d} \implies ad = bc\]
Do that.

Answer 5

for left side, if multiply it by conyugate of numerator gives
(1+Cosx)/sinx * (1-cosx)/(1-cosx) = (1-cos^2 x)/(sinx*(1-cosx))
= sin^2 x / (sinx*(1-cosx))
simplify again...

Answer 6

@scarydoor you cannot do that. this is a RHS--> LHS proof.

Answer 7

@Shadowys yes, you can do that.

Answer 8

............ you can't use something you haven't proved yet.

Answer 9

i dont think we can cross multiply while prooving @scarydoor

Answer 10

By using equivalently true statements, you can. You just need to be careful that the order of implications runs the right way. Above, I should have said "iff" not "implies", to avoid your complaint.

Answer 11

\[\frac{a}{b}=\frac{c}{d} \iff ad = bc.\]

Answer 12

you're trying to prove \(\frac{1+\cos x}{\sin x} = \frac{\sin x}{1-\cos x} \)

you don't know if \(\frac{1+\cos x}{\sin x} = \frac{\sin x}{1-\cos x} \)

if and only if\(\frac{1+\cos x}{\sin x} = \frac{\sin x}{1-\cos x} \) then \(\frac{1+\cos x}{\sin x} = \frac{\sin x}{1-\cos x} \)