Question 81

$$\frac{(1 + tan^{2}A)cotA}{cosec^{2}A}$$is equal to

Solution

Expression : $$\frac{(1 + tan^{2}A)cotA}{cosec^{2}A}$$

$$\because (sec^2A-tan^2A=1)$$

= $$\frac{sec^2AcotA}{cosec^2A}$$

= $$\frac{1}{cos^2A}\frac{cosA}{sinA}\div\frac{1}{sin^2A}$$

= $$\frac{1}{sinAcosA}\div\frac{1}{sin^2A}$$

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

= $$\frac{sinA}{cosA} = tanA$$

=> Ans - (B)

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