If is a n acute angle and tanx=3 4 evaluate cosx-sinx cosx+sinx
Oh, I see we're dealing with a trigonometry question here. Well, let's bring out the clownish math skills!
Since tan(x) = 3/4, we can use the Pythagorean identity to find the values of sin(x) and cos(x).
First, we'll let's call the adjacent side A and the opposite side O. We know that tan(x) = O/A = 3/4. So, let's assign A = 4 and O = 3.
Next, using the Pythagorean theorem, we can find the hypotenuse H:
H^2 = A^2 + O^2
H^2 = 4^2 + 3^2
H^2 = 16 + 9
H^2 = 25
H = 5
Now that we have the values for the sides of the right triangle, we can evaluate cos(x) and sin(x).
cos(x) = A/H = 4/5 and sin(x) = O/H = 3/5.
Finally, let's substitute these values into the expressions 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
So, the values of cos(x) - sin(x) and cos(x) + sin(x) are 1/5 and 7/5 respectively. Now, that's math with a hint of clownish humor!