If A is in the III quadrant- 3 tan A -4-0 then 5 sin 2 A -3 sin A -4 cos A -A- 0 B- -24-245D- 245-5

The correct option is A 0 Given tan A=4/3, A is in the III quadrant 5 sin 2A + 3 sin A + 4 cos A = 5(2 sin A cos A) + 3 sin A + 4 cos A =10 ( 4/5 ) ( 3/5 )+ ...

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Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

If A is in th...

Question

If A is in the III quadrant, 3 tan A –4 = 0 then 5 sin 2A + 3 sin A + 4 cos A=

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Solution

Given tan A= $\frac{4}{3}$ , A is in the III quadrant
5 sin 2A + 3 sin A + 4 cos A = 5(2 sin A cos A) + 3 sin A + 4 cos A
$= 10 (- \frac{4}{5}) (- \frac{3}{5}) + 3 (- \frac{4}{5}) + 4 (- \frac{3}{5}) = \frac{24}{5} - \frac{12}{5} - \frac{12}{5} = 0$

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Similar questions

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If A is in the III quadrant, 3 tan A –4 = 0 then 5 sin 2A + 3 sin A + 4 cos A=

Given tan A=43, A is in the III quadrant 5 sin 2A + 3 sin A + 4 cos A = 5(2 sin A cos A) + 3 sin A + 4 cos A =10(−45)(−35)+3(−45)+4(−35)=245−125−125=0

Given tan A= $\frac{4}{3}$ , A is in the III quadrant
5 sin 2A + 3 sin A + 4 cos A = 5(2 sin A cos A) + 3 sin A + 4 cos A
$= 10 (- \frac{4}{5}) (- \frac{3}{5}) + 3 (- \frac{4}{5}) + 4 (- \frac{3}{5}) = \frac{24}{5} - \frac{12}{5} - \frac{12}{5} = 0$