A) \[\text{6 cos A}\]
B) \[\text{6 sec A}\]
C) \[\text{6 sin A}\]
D) \[\text{tan A}\]
Correct Answer: A
Solution :
\[4\tan A+3\sin A=\frac{4\sin A}{\sqrt{1-{{\sin }^{2}}A}}+3\sin A\] \[=\frac{4\times \frac{3}{5}}{\sqrt{1-\frac{{{3}^{2}}}{{{5}^{2}}}}}+3\cdot \frac{3}{5}=\frac{12}{5}\times \frac{5}{4}+\frac{9}{5}=3+\frac{9}{5}=\frac{24}{5}\] \[\cos A=\sqrt{1-{{\sin }^{2}}A}=\frac{4}{5}\] \[6\cos A=6\left( \frac{4}{5} \right)=\frac{24}{5}\]
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