Simplify $$\sqrt\frac{1+cosA}{1-cosA}$$​

Correct option is C

Given:

​$$\sqrt\frac{1+cosA}{1-cosA}$$

Concept:

​$$\frac{1}{sinA}$$ = cosec A

​$$\frac{cosA}{sin A}$$ = cot A

Solution:

​$$\sqrt\frac{1+cosA}{1-cosA}$$

We multiply both the numerator and the denominator by 1+ cosA

​$$\sqrt\frac{(1+cosA)^2}{(1-cosA)(1+cosA)}$$

​​The denominator is now a difference of squares:

(1−cosA) (1+cosA) = $$1^2 - cos^2A = sin^2A$$

​​$$\sqrt\frac{(1+cosA)^2}{sin^2A}$$

$$\frac{1+cosA}{sinA}$$

$$\frac{1}{sinA}+\frac{cosA}{sinA}$$

cosecA + cotA

1+cos⁡A1 + \cos AThus, the correct option is (c) cosecA + cotA

​