Question

if 4tan A = 3 then,

4sinA-3cosA/4sinA+3cosA​

Answer 1

Step-by-step explanation:

if 4tan A = 3 then,

4sinA-3cosA/4sinA+3cosA

Answer 2

SOLUTION

GIVEN

4 tan A = 3

TO DETERMINE

$\displaystyle \sf{ \frac{4 \sin A - 3 \cos A }{4 \sin A + 3 \cos A } }$

EVALUATION

Here it is given that

4 tan A = 3

Now

$\displaystyle \sf{ \frac{4 \sin A - 3 \cos A }{4 \sin A + 3 \cos A } }$

Dividing both of the numerator and denominator by cos A we get

$\displaystyle \sf{ = \frac{4 \dfrac{\sin A}{ \cos A} - 3 \dfrac{ \cos A}{ \cos A} }{4 \dfrac{\sin A}{ \cos A} + 3 \dfrac{ \cos A}{ \cos A}} }$

$\displaystyle \sf{ = \frac{4 \tan A - 3}{4 \tan A + 3} }$

$\displaystyle \sf{ = \frac{3 - 3}{3 + 3} }$

$\displaystyle \sf{ = \frac{0}{6} }$

$\displaystyle \sf{ = 0 }$

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