Hello there,

Let we take angle Thita as 'x' . We have to prove that Sinx - Cosx +1 / Sinx + Cosx - 1 = 1/ Secx - Tanx

So now we will take the LHS of the question.

Now multiply the numerator and denominator by Sinx + Cosx +1

Now, our left side becames 1+ Sinx / Cosx

Now again multiply the numerator and denominator by 1- Sinx

So we get , Cosx / 1 - Sinx.

Now just divide the numerator and denominator by Cosx .

Hence We get 1/ Secx - Tanx

Hope it helps you.