Question

Sin Theta/1+Cos Theta + 1+Cos Theta/Sin Theta = 2 Cosec Theta . prove the identity.

Answer 1

Proving it will take quite a bit of work. You can verify it using other, more fundamental, identities.

Looks like you want to verify that
\[\large \frac{sin}{1+cos}+\frac{1+cos}{sin}=2csc\]

Answer 2

Try adding the fractions on the left (remember, you'll need a common denominator), then simplify that.

Answer 3

@CliffSedge can write the 1st step, i'm really don't understand ..

Answer 4

I like the "bow-tie" method for adding fractions.
\[\large \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]

Answer 5

a=d=sin(Θ)
b=c=1+cos(Θ)

Answer 6

if bd = ? @CliffSedge

Answer 7

bd=sin(1+cos)

Answer 8

\[\large \frac{sin}{1+cos}+\frac{1+cos}{sin}=\frac{sin^2+(1+cos)^2}{sin(1+cos)}\]

Answer 9

Simplify the top and you'll see what can cancel in the bottom.

Answer 10

alright i got already . thanks :) @CliffSedge im trying to do first ..