If x is an acute angle, tanx =3/4,evaluate coax _sinx÷cosx+sinx
geez - take care with your expressions.
divide top and bottom by cosx, Then you have
(cosx-sinx)/(cosx+sinx) = (1-tanx)/(1+tanx) = (1/4)/(7/4) = 1/7
extra credit: why does it matter that x is acute?
If x is an acute angle and tan x 3/4,evaluate cos x _ sin x / cos x + sin x
Thanks but need to elaborate on the question cause the method you used might not make the people that need to use it understand better
Thanks you
Pls explain better
Please explain further
ajagbokun
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Solve the math
If x is an acute angle and tanx= 3/4 evaluate cosx-sinx sinx +cosx
To evaluate the expression `cosec(x) / cos(x) + sin(x)`, we'll start by determining the values of `cosec(x)`, `cos(x)`, and `sin(x)` based on the given information.
Given that `tan(x) = 3/4`, we can solve for `sin(x)` and `cos(x)` using the trigonometric identity `tan(x) = sin(x) / cos(x)`.
1. Start by rewriting `tan(x) = 3/4` as an equation involving sine and cosine:
`3/4 = sin(x) / cos(x)`
2. Rearrange the equation to isolate `sin(x)`:
`sin(x) = (3/4) * cos(x)`
3. Since cosine is the adjacent side divided by the hypotenuse in a right triangle, the value of the adjacent and hypotenuse sides can be represented using the Pythagorean theorem. Let's assume `cos(x) = a` and `sin(x) = b`. Hence:
`(a^2 + b^2) = 1`
4. Substituting `a` with `cos(x)` and `b` with `(3/4) * cos(x)`, we have:
`(cos(x))^2 + (3/4 * cos(x))^2 = 1`
5. Simplify the equation:
`16 cos²(x) + 9 cos²(x) = 16`
`25 cos²(x) = 16`
`cos²(x) = 16/25`
6. Taking the square root of both sides:
`cos(x) = ± √(16/25)`
`cos(x) = ± (4/5)`
Since `x` is an acute angle, `cos(x)` is positive. Therefore, `cos(x) = 4/5`.
To find `sin(x)`, we can substitute `cos(x) = 4/5` into the equation `sin(x) = (3/4) * cos(x)` from step 2:
`sin(x) = (3/4) * (4/5)`
`sin(x) = 3/5`
Now that we have the values of `sin(x)` and `cos(x)`, we can evaluate the expression `cosec(x) / cos(x) + sin(x)`:
`cosec(x) / cos(x) + sin(x) = (1 / sin(x)) / cos(x) + sin(x)`
Since `cosec(x)` is the reciprocal of `sin(x)`, we'll substitute `cosec(x) = 1 / sin(x)`:
`(1 / sin(x)) / cos(x) + sin(x) = (1 / sin(x)) / cos(x) + sin(x)`
Next, substitute the known values of `sin(x)` and `cos(x)`:
`[(1 / (3/5)) / (4/5)] + 3/5`
Simplifying the expression further:
`[(5/3) / (4/5)] + 3/5 = [(5/3) * (5/4)] + 3/5`
Multiply the fractions:
`[(25/12)] + 3/5`
To combine the fractions, find a common denominator:
`[(25/12) * (5/5)] + (3/5 * (12/12)) = (125/60) + (36/60)`
Adding the fractions:
`125/60 + 36/60 = 161/60`
Thus, the value of `cosec(x) / cos(x) + sin(x)` is `161/60`.