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## Homework Statement

I was solving a problem involving sine and cosine ratios.

If I come to know the maximum possible value of (sin x+cos x), x belongs to [0,2*pi]. my problm would be solved.

## Homework Equations

## The Attempt at a Solution

I think x ill be in 1st quadrant as both sin and cos are +ve. If I am not wrong x=45????

but how do i mathematically prove

this?