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In your mind, what are you thinking about “What is max value of sinx + cosx”

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To get the max or min value of a function we differentiate it twice. We equate the first differentiation to 0 as the slope of max or min point on a graph will have its slope equal to 0 and we check the sign of second differentiate. If it is negative then the value is max else min.

Another way of seeing this is by drawing the unit circle, and picking any point on the circle. Then draw a vertical line segment to the horizontal axis, and a horizontal line segment to the vertical axis. The area of the rectangle you just drew will be equal to [math]f(\theta)[/math] where [math]\theta[/math] is the angle corresponding to the point you chose.

You can dissect this inquiry as x<tanx for (π/2,3π/2). For what reason did this occur? Since we partitioned the two sides with cosx and since in the given span it is non zero we are legitimate in doing as such; yet we notice that cosx itself is negative in the given space, subsequently separating by a negative amount changes the disparity.

Presently by charting the two capabilities you can without much of a stretch see that they meet at a certain point (4.493,4.493) in the space , before which x is more noteworthy than tanx and after which it is lesser.

In spite of the fact that getting the fact of the matter is a piece extreme (you need to involve Newton's technique for tackling non-straight conditions) however atleast you can gauge it utilizing charts. So answer would be approx. (4.493,3π/2).