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Choose the correct answer in each of the following questions: If `7tan theta=4 " then " ((7sin theta - 3 cos theta))/((7sin theta + 3 cos theta))=?`

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Choose the correct answer in each of the following questions:
If `7tan theta=4 " then " ((7sin theta - 3 cos theta))/((7sin theta + 3 cos theta))=?`
A. `(1)/(7)`
B. `(5)/(7)`
C. `(3)/(7)`
D. `(5)/(17)`

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Correct Answer - A
Given, `tan theta =(4)/(7).`
`therefore ((7sintheta-3costheta))/((7sintheta+3costheta))=((7tan theta-3))/((7tan theta+3)) " "["dividing num. and denom. by "costheta]`
`=((7xx(4)/(7)-3))/((7xx(4)/(7)+3))=((4-3))/((4+3))=(1)/(7).`
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