Question

12
12. If sin theta = 12/13 then evaluate (2sin theta -3cos theta/4sin thrta -9cos theta)​

Answer 1

Answer:

Solution

$\sin( \alpha ) = \frac{12}{13} \\ \cos( \alpha ) = \sqrt{1 - \sin( ^{2} ) } \\ = \sqrt{1 - ( \frac{12}{13} } ) ^{2} \\ = \sqrt{1 - \frac{144}{169} } \\ = \sqrt{ \frac{169 - 144}{144} } \\ = \sqrt{ \frac{25}{169} } \\ = \frac{5}{13} \\ \\ \\ \frac{2 \sin( \alpha ) -3 \cos( \alpha ) }{4 \sin( \alpha ) - 9 \cos( \alpha ) } \\ = \frac{2 \times \frac{12}{13} - 3 \times \frac{5}{13} }{4 \times \frac{12}{13} - 9 \times \frac{5}{13} } \\ = \frac{ \frac{24}{13} - \frac{15}{13} }{ \frac{48}{13} - \frac{45}{13} } \\ = \frac{ \frac{24 - 15}{13} }{ \frac{48 - 45}{13} } \\ = \frac{9}{3} \\ = 3$

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