if x is an acute angle and tan x --3/4 evaluate : cos x sin x /cos. x + sin x
I need the answer
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 (somewhat ambiguous) expression
To evaluate the expression cos x sin x / (cos x + sin x), we'll use the properties of trigonometric functions and manipulate the expression to simplify it further.
Given that tan x = -3/4, we can start by using the definition of tangent as the ratio of sine to cosine:
tan x = sin x / cos x = -3/4
From this, we can deduce that sin x = -3k and cos x = 4k, where k is a positive constant. This substitution makes the expression:
cos x sin x / (cos x + sin x) = (4k)(-3k) / (4k - 3k)
Simplifying this further, we get:
-12k^2 / k = -12k
Therefore, the evaluated expression is -12k.