If is a n acute angle and tanx=3 4 evaluate cosx-sinx cosx+sinx
To find the values of cos(x) - sin(x) and cos(x) + sin(x), we first need to find the values of cosine and sine functions for the angle x. Given that tan(x) = 3/4, we can use the Pythagorean identity to find the values of cosine and sine.
1. Start by drawing a right triangle with an acute angle x.
2. Given that tan(x) = opposite/adjacent = 3/4, let's assign the opposite side to be 3 (let's call it y) and the adjacent side to be 4 (let's call it x).
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3 | /x
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3. Using the Pythagorean theorem, find the hypotenuse (h).
h^2 = x^2 + y^2
h^2 = 4^2 + 3^2
h^2 = 16 + 9
h^2 = 25
h = 5
4. Now we have the values of the adjacent side (x = 4) and the hypotenuse (h = 5). We can use these values to find cosine and sine.
cosine(x) = adjacent/hypotenuse = 4/5
sine(x) = opposite/hypotenuse = 3/5
5. Now that we have the values of cosine(x) and sine(x), we can evaluate cos(x) - sin(x) and cos(x) + sin(x).
cos(x) - sin(x) = (4/5) - (3/5) = 1/5
cos(x) + sin(x) = (4/5) + (3/5) = 7/5
Therefore, cos(x) - sin(x) = 1/5 and cos(x) + sin(x) = 7/5.