$\frac{\sqrt{cosecx-1}}{\sqrt{cosecx+1}}$ is equal to:
Answer & explanation
Correct answer: option 1
$\frac{\sqrt{cosecx-1}}{\sqrt{cosecx+1}}$
= $\frac{\sqrt{1/sinx-1}}{\sqrt{1/sinx+1}}$
= $\frac{\sqrt{1-sinx}}{\sqrt{1+sinx}}$
multiply and divide by \(\sqrt {1-sinx }\)
= $\frac{\sqrt{1-sinx}}{\sqrt{1+sinx}}$ × $\frac{\sqrt{1-sinx}}{\sqrt{1-sinx}}$
= $\frac{\sqrt{(1-sinx)²}}{\sqrt{1-sin²x}}$
{ sin²θ + cos²θ = 1 }
= $\frac{\sqrt{(1-sinx)²}}{\sqrt{cos²x}}$
= \(\frac{1 -sinx }{cosx}\)
= secx - tanx