Question

if 4 tan A =3 then find the value of 4sinA - cosA/4sinA + cos A​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The value of given expression is

$\frac{4sinA - cosA}{4sinA + cosA} = \frac{1}{2}$

Step-by-step explanation:

Given that,

$4tanA=3 = > tanA= \frac{3}{4}$

Therefore,the opposite side of the angle A is 3 units and its adjacent side is 4 units.The hypotenuse is

$\sqrt{3 {}^{2} + {4}^{2} } = 5 \: units$

Now we find the values of sinA and cosA as follows

$sinA = \frac{opposite}{hypotenuse} = \frac{3}{5} \\ cosA = \frac{adjacent}{hypotenuse} = \frac{4}{5}$

Our given equation is

$\frac{4sinA - cosA}{4sinA + cosA}$

Substituting the known values we get the value as

$\frac{4( \frac{3}{5} ) - \frac{4}{5} }{4( \frac{3}{5}) + \frac{4}{5} } = \frac{8}{16} = \frac{1}{2}$

Therefore,the value of given expression is

$\frac{4sinA - cosA}{4sinA + cosA} = \frac{1}{2}$

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