Question

Prove that
sinθ - cosθ +1 / sinθ + cosθ - 1 = 1 / secθ + tanθ - 1

Please prove it correctly.​

Answer 1

Answer:

L. H. S is not equal to R. H. S

Step-by-step explanation:

Taking L. H. S

sinθ - cosθ +1 / sinθ + cosθ - 1

We know that sinθ + cosθ = 1

So,

sinθ - cosθ + sinθ + cosθ / sinθ + cosθ - (sinθ + cosθ)

sinθ - cosθ + sinθ + cosθ / sinθ + cosθ - sinθ - cosθ

In which both positive or negative values cancel to each.

Then, it give;

2sinθ

Taking R. H. S

1 / secθ + tanθ - 1

We know that secθ = 1/cosθ & tanθ = sinθ/cosθ

So;

1/ 1/cosθ + sinθ/cosθ

1/ 1+sinθ - cosθ/cosθ

1/ cosθ / 1+sinθ - cosθ

We know that sinθ + cosθ=1

1/ cosθ / sinθ + cosθ + sinθ - cosθ

1/ cosθ/ 2sinθ

2sinθ / cosθ