Question

sin A/1-cot A+cos A/1-tan A​

Answer 1

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• Find :-
• $\mathtt{ \frac{sinA}{1 - cotA} + \frac{cosA}{1 - tanA} }$

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• $\mathtt{ \frac{sinA}{1 - cotA} + \frac{cosA}{1 - tanA} } \\ \\ \mathtt{ \frac{sinA}{1 - \frac{cosA}{sinA} } + \frac{cosA}{1 - \frac{sinA}{cosA} } } \\ \\ \mathtt{ \frac{sinA}{ \frac{sinA - cosA}{sinA} } + \frac{cosA}{ \frac{cosA - sinA }{cosA} } } \\ \\ \mathtt{ \frac{sin {}^{2}A }{(sinA - cosA) } - \frac{cos {}^{2} A}{(sinA - cosA)} } \\ \\ \mathtt{ \frac{sin {}^{2}A - cos {}^{2} A}{(sinA - cosA)} } \\ \\ \mathtt{ \frac{(sinA - cosA)(sinA + cosA)}{(sinA - cosA)} } \\ \\ \mathtt{ \frac{ \cancel{(sinA - cosA)}(sinA + cosA)}{ \cancel{(sinA - cosA)}} } \\ \\ \underline{ \underline{\mathtt{(sinA + cosA)}}}$