Prove that sinA/1-cosA =1 +cosA/sinA

To prove sinA/(1-cosA) = (1+cosA)/sinA.

Proof:

we know that,

sin^2 A+cos^2 A= 1, is a trigonometric identity.

Therefore,

sin^2 A = 1- cos^2 A  = (1+cosA)(1-cosA). So,

Sin^2 A /(1-cosA) = 1+cosA  or

sinA/(1-cosA) = (1+cosA)/sinA.

Note:

The original problem is  sinA/1-cosA = 1+cosA/sinA. This is not an identity, for,

SinA/1-cosA  = 1+cosA/sinA. This means:

Put A= 0 deg. Then,

LHS = sin 0 /1 -cos0) = 1/1 - 1 = 1 -1 = 0 .

RHS= 1 + cos 0 / sin 0 = 1+1/0 = infinite.

Therefore, it is edited to read as:

Prove sinA/(1-cosA) = (1+cosA)/sinA.