Question
Let f:RβR be defined as f(x) = cosx + sinx. Then the
range of f(x) is:ΒSolution
We are given the function f(x) = cosx + sinx , and asked to find its range . To determine the range, observe that this is a standard form of a trigonometric identity. We can write: f(x) = cosx + sinx = β2{(cosx / β2) + (sinx/β2)} = β2 sin(x+Ο/4)
This uses the identity: 
Where tan Ο = b/a. In our case, a = 1, b = 1, so: f(x) = β2 sin(x+Ο/4)
Since sin(ΞΈ) always lies in [β1,1], it follows that: f(x) = β2 sin(x+Ο/4) β [β2β,2β].
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