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Question

Prove that $$\dfrac{\cot{A}-\cos{A}}{\cot{ A}+ \cos{ A }}=\dfrac{\csc{A}-1}{\csc{ A}+1}$$


Solution

$$\frac{cot A- cos A}{cot A + cos A}= \frac{cosec A-1}{cosec +1}$$
on solving LHS are get
$$\frac{\frac{cos A}{sin A}- cos A}{\frac{cos A}{sin A}+cos A}=\frac{cos (\frac{1}{sin A}-1)}{cos A (\frac{1}{sin A})+1}[\because \frac{1}{sin A}= cosec A]$$
$$\frac{cosec A-1}{cosec A+1}= RHS$$

1188810_1366305_ans_7a9ff4d3e1934ec79497b261e705cb31.JPG

Mathematics

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