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Question: If 0 \< x \< 1, then \(\sqrt { 1 + \mathrm { x } ^ { 2 } }\) [{cos(cot<sup>–1</sup>x) + sin (cot<s...

If 0 < x < 1,

then 1+x2\sqrt { 1 + \mathrm { x } ^ { 2 } } [{cos(cot–1x) + sin (cot–1x)}2 – 1]1/2 is equal to

A

B

x

C

x

D

Answer

x

Explanation

Solution

[{x cos(cot–1x) + sin(cot–1x)}2 – 1]1/2

1+x2\sqrt { 1 + x ^ { 2 } } [(x21+x2+11+x2)2−1]1/2\left[ \left( \frac { x ^ { 2 } } { \sqrt { 1 + x ^ { 2 } } } + \frac { 1 } { \sqrt { 1 + x ^ { 2 } } } \right) ^ { 2 } - 1 \right] ^ { 1 / 2 }

= x