The value of (cosec A + cot A) (1 – cos A) is:

Correct option is A

Given: ​

​$$(\cosec A + \cot A) (1 – \cos A)$$ 

Formula Used:

Trigonometric identities:

​$$\cosec A = \frac{1}{\sin A}\\ \ \\\cot A = \frac{\cos A}{\sin A}\\ \ \\\sin^2A + \cos^2A = 1\\ \ \\a^2 – b^2 = (a-b)(a+c)$$​​

Solution:

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