If $ \theta $ lies in the second quadrant and $ 3 \tan \theta+4=0 $, then the value of $ 2 \cot \theta-5 \cos \theta+\sin \theta $ is $ \frac{6}{k} $ then find $ k $.

Question

If $ \theta $ lies in the second quadrant and $ 3 \tan \theta+4=0 $, then the value of $ 2 \cot \theta-5 \cos \theta+\sin \theta $ is $ \frac{6}{k} $ then find $ k $.,

MARKS App · Accepted Answer

3 tan θ + 4 = 0 ⇒ tan θ = - 4 3 cot θ = - 3 / 4 cos θ = - 3 / 5 sin θ = 4 / 5 = 2 cot θ - 5 cos θ + sin θ = 2 ( - 3 / 4 ) - 5 ( - 3 / 5 ) + 4 / 5 = 23 10

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