Question

If $\cos \theta =\frac{2}{3}$, then the value of $2\sec \theta +4{\tan }^2\theta -7$ is equal to

• A. $1$
• B. $0$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$\cos \theta =\frac{2}{3}\Rightarrow \sec \theta =\frac{1}{\cos \theta }=\frac{3}{2}$

$\Rightarrow 2\sec \theta +4{\tan }^2\theta -7=2\times \frac{3}{2}+4({\sec }^2\theta -1)-7$

$=3+4(\frac{9}{4}-1)-7$

$=4\times \frac{5}{4}-4$

$=5-4$

$=1$

Hence, the answer is $1.$