Question

If tan =3/4 , find the value of 3sin +2cos /3sin - 2cos​

Answer 1

Answer:

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Answer 2

17

Step-by-step explanation:

Given: $tan\theta =\frac{3}{4}$

To find: Value of $\frac{3\:sin+2\:cos}{3\:sin-2\:cos}$

Solution:

$tan\theta =\frac{3}{4}$

$\implies \frac {Perpendicular}{Base}=\frac{3x}{4x}$

Now, using Pythagoras's theorem;

(Hypotenuse)² = (Perpendicular)² + (Base)²

(Hypotenuse)² = (3x)² + (4x)²

= 9x² + 16x²

= 25x²

Hypotenuse = √25x²

$\implies$ Hypotenuse = 5x

Now, $sin\theta = \frac{Perpendicular}{Hypotenuse}=\frac{3x}{5x}={3}{5}$

$cos\theta = \frac{Base}{Hypotenuse}=\frac{4x}{5x}=\frac{4}{5}$

$\frac{3\: sin\theta+ 2\:cos\theta}{3\:sin\theta-2\:cos\theta}$

Putting values;

$\implies \frac{3(\frac{3}{5})+2(\frac{4}{5})}{3(\frac{3}{5})-2(\frac{4}{5})}$

$\implies \frac{\frac{9}{5}+\frac{8}{5}}{\frac{9}{5}-\frac{8}{5}}$

$\implies \frac{\frac{17}{5}}{\frac{1}{5}}$

$\implies \frac{17}{5}\times \frac{5}{1}$

$= 17$