Question 89

If cosecA + cotA = x, then value of x is

Solution

Expression : cosecA + cotA = x

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

Multiplying both numerator and denominator by $$(1-cosA)$$

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

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

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

Dividing both numerator and denominator by $$(sinA)$$

= $$\frac{1}{cosecA-cotA}$$

=> Ans - (A)

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