A) \[\frac{3}{5}\]
B) \[\frac{3}{4}\]
C) \[\frac{4}{3}\]
D) \[\frac{5}{3}\]
Correct Answer: B
Solution :
| [b] Given, \[\cos A=4/5\] |
| \[\sin A=\sqrt{1-{{\cos }^{2}}A}\]\[[{{\sin }^{2}}A+{{\cos }^{2}}A=1]\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\sin A=\sqrt{1-{{\left( \frac{4}{5} \right)}^{2}}}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}\] |
| Now, \[\tan A=\frac{\sin A}{\cos A}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}\] |
| Hence, the required value of tan A is \[3/4\]. |
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