Question 38

What is the value of $$\sqrt{[\frac{(1 - cosA)}{(1 + cosA)}}]$$?

Solution

Expression : $$\sqrt{[\frac{(1 - cosA)}{(1 + cosA)}}]$$

Multiplying both numerator and denominator by $$\sqrt{(1-cosA)}$$

= $$\sqrt{\frac{1-cosA}{1+cosA}} \times \sqrt{\frac{(1-cosA)}{(1-cosA)}}$$

= $$\sqrt{\frac{(1-cosA)^2}{1-cos^2A}} = \sqrt{\frac{(1-cosA)^2}{sin^2A}}$$

= $$\frac{1-cosA}{sinA} = \frac{1}{sinA}-\frac{cosA}{sinA}$$

= $$cosecA-cotA$$

=> Ans - (A)

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