Question

cos invers (cosx+sinx)/root2

Answer 1

Hi...☺

Here is your answer...✌

${ \cos }^{ - 1} ( \frac{ \cos x + \sin x}{ \sqrt{2} } ) \\ \\ = { \cos }^{ - 1} ( \: \frac{ 1}{ \sqrt{2}}\cos x + \frac{1}{ \sqrt{2} }\sin x \: ) \\ \\ = { \cos }^{ - 1} ( \:\cos \frac{\pi}{4} \cos x + \sin \frac{\pi}{4} \: \sin x \: ) \\ \\ = { \cos }^{ - 1} ( \:\cos ( \frac{\pi}{4} - x) \: ) \\ \\ = \frac{\pi}{4} - x$