Question

solve this question​

Answer 1

Answer →

→x = cot 2x

Step - by - step explanation:-

$</u><u>A</u><u>.</u><u>T</u><u>.</u><u>Q</u><u>.</u><u> \\ \\ {tan}^{ - 1} \frac{1 - x}{1 + x} = \frac{1}{2} {tan}^{ - 1} x \\ </u><u>\</u><u>\</u><u> </u><u> \because \:tan \: \frac{ \pi}{4} = 1 \\ </u><u>\</u><u>\</u><u> \: </u><u>H</u><u>ence </u><u>,</u><u>\\ \\ {tan}^{ - 1} \frac{tan \frac{ \pi}{4} - x}{1 + tan \frac{ \pi}{4} \: x} = \frac{1}{2} {tan}^{ - 1} x \\ \\ \because \: tan(a - b) = \frac{tan \: a - tan \: b}{1 + tan \: a \: tn \: b} \\ \\ </u><u>T</u><u>herefore </u><u>,</u><u>\\ \\ {tan}^{ - 1} tan( \frac{ \pi}{4} - x) = \frac{1}{2} {tan}^{ - 1} x \\ \\ \frac{ \pi}{4} - x = \frac{1}{2} {tan}^{ - 1}x \\ \\ \frac{ \pi}{2} - 2x = {tan}^{ - 1} x \\ \\ \</u><u>t</u><u>herefore x = tan \: \bigg( \frac{ \pi}{2} - 2x \bigg) \\ \\ \implies \: \boxed{ x = cot \: 2x} \\ \\ \because \: tan(90 \degree - \theta) = cot \theta$