Question

if 3 cos theta = 2 Sin Theta then the value of 4 sin theta minus 3 cos theta divided by 2 sin theta + cos theta

Answer 1

By using above method, it can be solved by this way.

Answer 2

Hope u like my process
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Given:

$3 \cos( \theta ) = 2 \sin( \theta ) \\ \\ or. \: \: \frac{ \sin( \theta ) }{ \cos( \theta ) } = \frac{3}{2} \\ \\ or. \: \tan( \theta ) = \frac{3}{2} = 1.5$
Now..

$\frac{4 \sin( \theta ) - 3 \cos( \theta ) }{2 \sin( \theta ) + \cos( \theta ) } \\ \\ = \frac{4 \sin( \theta ) - 3 \cos( \theta ) }{2 \sin( \theta ) + \cos( \theta ) } \times \frac{ \cos( \theta ) }{ \cos( \theta ) } \\ \\ = \frac{ \frac{4 \sin( \theta ) - 3 \cos( \theta ) }{ \cos( \theta ) } }{ \frac{2 \sin( \theta ) + \cos( \theta ) }{ \cos( \theta ) } } \\ \\ = \frac{4 \tan( \theta ) - 3}{2 \tan( \theta ) + 1 } \\ \\ = \frac{4(1.5) - 3}{2(1.5) + 1} = \frac{6 - 3}{3 + 1} \\ \\ = \frac{3}{4}$
Hope this is ur required answer

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