Question 91

What is the value of sinAtanA/(1 - cosA)?

Solution

Expression : $$\frac{sin A tan A}{1 - cos A}$$

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

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

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

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

=> Ans - (B)

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