Question

Choose the correct answer in each of the following questions:
If `3cot theta =4 " then " ((5 sin theta + 3 cos theta))/((5 sin theta-3 cos theta))=?`
A. `(1)/(3)`
B. 3
C. `(1)/(9)`
D. 9

Answer 1

Correct Answer - D
Given, `cot theta=(4)/(3).`
`therefore ((5sintheta+3costheta))/((5sintheta-3costheta))=(5+3cot theta)/(5-3cot theta) " "["dividing num. and denom. by "sintheta]`
`=((5+3xx(4)/(3)))/((5-3xx(4)/(3)))=((5+4))/((5-4))=(9)/(1)=9.`