dear student LHS = 1cosec A - cot A - 1sin A=1cosec A - cot A×cosec A + cot Acosec A + cot A - 1sin A=cosec A + cot Acosec2A - cot2A - 1sin A=cosec A + cot A1 - 1sin A=cosec A + cot A - cosec A= cot A RHS = 1sin A - 1cosec A + cot A=1sin A - 1cosec A + cot A ×cosec A - cot Acosec A - cot A=1sin A - cosec A - cot Acosec2A - cot2A=1sin A - cosec A - cot A1=1sin A - cosec A - cot A=cosec A - cosec A + cot A=cot ASo, LHS = RHS regards

Pl solve this sir

dear student

LHS = \frac{1}{cosec A - \cot A} - \frac{1}{\sin A} = \frac{1}{cosec A - \cot A} \times \frac{cosec A + \cot A}{cosec A + \cot A} - \frac{1}{\sin A} = \frac{cosec A + \cot A}{{cosec}^{2} A - \cot^{2} A} - \frac{1}{\sin A} = \frac{cosec A + \cot A}{1} - \frac{1}{\sin A} = cosec A + \cot A - cosec A = \cot A

RHS = \frac{1}{\sin A} - \frac{1}{cosec A + \cot A} = \frac{1}{\sin A} - \frac{1}{cosec A + \cot A} \times \frac{cosec A - \cot A}{cosec A - \cot A} = \frac{1}{\sin A} - \frac{cosec A - \cot A}{{cosec}^{2} A - \cot^{2} A} = \frac{1}{\sin A} - \frac{cosec A - \cot A}{1} = \frac{1}{\sin A} - (cosec A - \cot A) = cosec A - cosec A + \cot A = \cot A So, LHS = RHS

regards

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