Question 35

If $$\frac{\sqrt{(1+cot^{2}A)}}{CotA}=x$$, then the value of x is

Solution

Expression : $$\frac{\sqrt{1 + cot^2 A}}{cot A}$$

= $$\sqrt{1 + \frac{cos^2 A}{sin^2 A}} \times \frac{1}{cot A}$$

= $$\sqrt{\frac{sin^2 A + cos^2 A}{sin^2 A}} \times \frac{1}{cot A}$$

= $$\sqrt{\frac{1}{sin^2 A}} \times \frac{1}{cot A}$$

= $$\frac{1}{sin A} \times \frac{sin A}{cos A}$$

= $$\frac{1}{cos A} = sec A$$

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