Question

solve sin x+cos x=1/root2​

Answer 1

Here's the solution required for your problem

Answer 2

$\sin(x) + \cos(x) = \frac{1}{ \sqrt{2} } \\ squaring \: both \: sides \\ ( \sin(x) + \cos(x) )^{2} = ( \frac{1}{ \sqrt{2} })^{2} \\ { \sin^{2} (x) } + \cos^{2}( x) + 2. \sin(x) . \cos(x) = \frac{1}{2} \\ 1 + 2. \sin(x) .\cos(x) = \frac{1}{2} \\ 2. \sin(x) . \cos(x) = \frac{1}{2} - 1 \\ \sin(2x) = - \frac{1}{2} \\ 2x = 210 \: degrees \\ therefore \: x = 105 \: degrees$

Hope you found what you were looking for.. please let me know if it's incorrect or not what you were looking for in the comments below..
Thanks