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  • If and x  is in the first quadrant, find the value of <img a

If sec\ x=\frac{4}{3} and x  is in the first quadrant, find the value of tan\ x. 

Option: 1

\sqrt{ \frac{7}{9}}


Option: 2

-\sqrt{ \frac{7}{9}}


Option: 3

\sqrt{ \frac{5}{9}}


Option: 4

-\sqrt{ \frac{5}{9}}


Answers (1)

best_answer

Answer: Option (a) \sqrt{ \frac{7}{9}} 

Explanation: 

Given that,

sec\ x=\frac{4}{3}

Using the tangent formula,

tan\ x=\pm \sqrt{sec^{2}x-1}

Since x is in the first quadrant, cos\ x is positive. Thus,

Substituting the value of sec\ x=\frac{4}{3} to get,

tan\ x=\pm \sqrt{\left ( \frac{4}{3} \right )^{2}-1}
tan\ x=\sqrt{ \frac{7}{9}}

Posted by

Gautam harsolia

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