Question 82

If $$(cotA - cosecA)^2 = x$$, then the value of x is

Solution

Expression : $$(cotA - cosecA)^2 = x$$

= $$(\frac{cosA}{sinA}-\frac{1}{sinA})^2$$

= $$(\frac{cosA-1}{sinA})^2$$

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

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

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

=> Ans - (A)

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