Question 74

$$(\operatorname{cosec}A-\cot A)(1+\cos A)=?$$

Solution

$$(\operatorname{cosec}A-\cot A)(1+\cos A)=\left(\frac{1}{\sin A}-\frac{\cos A}{\sin A}\right)\left(1+\cos A\right)$$

= $$\left(\frac{1-\cos A}{\sin A}\right)\left(1+\cos A\right)$$

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

= $$\frac{\sin^2A}{\sin A}$$

= $$\sin A$$

Hence, the correct answer is Option B

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