The value of (operatorname{cosec} a - sin a)( | vedclass

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Question

(A) Given expression: $(\operatorname{cosec} a - \sin a)(\sec a - \cos a)(	an a + \cot a)$Step $1$: Convert all trigonometric functions into $\sin a$

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$1$

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(A) Given expression: $(\operatorname{cosec} a - \sin a)(\sec a - \cos a)(	an a + \cot a)$Step $1$: Convert all trigonometric functions into $\sin a$ and $\cos a$.$= \left(\frac{1}{\sin a} - \sin aight) \left(\frac{1}{\cos a} - \cos aight) \left(\frac{\sin a}{\cos a} + \frac{\cos a}{\sin a}ight)$Step $2$: Simplify each bracket.$= \left(\frac{1 - \sin^2 a}{\sin a}ight) \left(\frac{1 - \cos^2 a}{\cos a}ight) \left(\frac{\sin^2 a + \cos^2 a}{\sin a \cos a}ight)$Step $3$: Use the identity $\sin^2 a + \cos^2 a = 1$.$= \left(\frac{\cos^2 a}{\sin a}ight) \left(\frac{\sin^2 a}{\cos a}ight) \left(\frac{1}{\sin a \cos a}ight)$Step $4$: Multiply the terms.$= \frac{\cos^2 a \cdot \sin^2 a}{\sin a \cdot \cos a \cdot \sin a \cdot \cos a} = \frac{\sin^2 a \cdot \cos^2 a}{\sin^2 a \cdot \cos^2 a} = 1$

The value of $(\operatorname{cosec} a - \sin a)(\sec a - \cos a)(\tan a + \cot a)$ is:

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