If x is an acute angle and tan x = 3/4
Evaluate : cos x - sin x
cos x + sin x
tanx = 3/4
draw the triangle, and you can see that the hypotenuse is 5, so
sinx = 3/5
cosx = 4/5
Now just use those values in your expression.
Help me to work it out
I don't understand
Word~bard
To evaluate cos x - sin x, we need to find the values of cos x and sin x using the given information.
We are given that tan x = 3/4. Since tan x is the ratio of sin x to cos x, we can use this information to find the values of sin x and cos x.
Using the Pythagorean identity, sin^2x + cos^2x = 1, we can substitute the value of tan x into the equation and solve for the values of sin x and cos x.
(tan x)^2 + 1 = (3/4)^2 + 1 = 9/16 + 1 = 25/16
Now, taking the square root of both sides to isolate sin x and cos x:
sin x = sqrt(1 - cos^2x)
cos x = sqrt(1 - sin^2x)
Note that x is an acute angle, so both sin x and cos x are positive. Therefore, we can take the positive square root in both cases.
sin x = sqrt(1 - (25/16)) = sqrt(16 - 25)/4 = -9/4 (This is negative, but we will use the positive value since sin is positive in the first quadrant.)
cos x = sqrt(1 - (9/16)) = sqrt(16 - 9)/4 = 7/4
Now we can substitute the values of sin x and cos x into the expressions:
cos x - sin x = (7/4) - (-9/4) = 7/4 + 9/4 = 16/4 = 4
cos x + sin x = (7/4) + (-9/4) = 7/4 - 9/4 = -2/4 = -1/2
Therefore, cos x - sin x = 4 and cos x + sin x = -1/2.