Question

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

Answer 1

Answer:

the answer is as follows

I hope this will help you

Answer 2

$Given \: sin \theta = \frac{12}{13} \: --(1)$

/* By Trigonometric Identity */

$\boxed{\pink{ cos^{2} \theta = 1 - sin^{2} \theta }}$

$i) Cos^{2} \theta$

$= 1 - sin^{2} \theta$

$= 1 - \Big( \frac{12}{13}\Big)^{2}$

$= 1 - \frac{144}{169}$

$= \frac{169 - 144}{169}$

$= \frac{25}{169}$

$ii ) \blue {cos \theta}$

$= \sqrt{ \Big( \frac{25}{169}\Big)}$

$\blue {= \frac{5}{13} }\: --(2)$

$Now , \red { Value \:of \: \frac{2sin \theta - 3cos \theta }{ 4sin \theta - 9 cos \theta } }$

$= \frac{ 2 \times \frac{12}{13} - 3 \times \frac{5}{13}}{ 4 \times \frac{12}{13} - 9 \times \frac{5}{13}}$

$= \frac{ \frac{24}{13} - \frac{15}{13}}{\frac{48}{13} - \frac{45}{13}}$

$= \frac{\frac{24-15}{\cancel {13}}}{\frac{48-45}{\cancel {13}}}$

$= \frac{ 9}{3}$

$= 3$

Therefore.,

$\red { Value \:of \: \frac{2sin \theta - 3cos \theta }{ 4sin \theta - 9 cos \theta } }\green { = 3 }$

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