Question

If $(2\tan \theta +1)(3\tan \theta +4)=11\tan \theta +5{\sec }^2\theta and{0}^{\circ }<\theta <{90}^{\circ },$ then the measure of $\theta$ is

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Answer 1

The correct option is B 45°

Given: $(2\tan \theta +1)(3\tan \theta +4)=11\tan \theta +5{\sec }^2\theta ,0^{\circ }<\theta <{90}^{\circ }$

$\Rightarrow 6{\tan }^2\theta +11\tan \theta +4=11\tan \theta +5(1+{\tan }^2\theta )$ $(\because 1+{\tan }^2\theta ={\sec }^2\theta )$

$\Rightarrow 6{\tan }^2\theta +4=5+5{\tan }^2\theta$

$\Rightarrow {\tan }^2\theta =1$

$\Rightarrow \tan \theta =\pm 1$

Given that $0^{\circ }<\theta <{90}^{\circ }$

$\Rightarrow \tan \theta =1=\tan {45}^{\circ }$

$\Rightarrow \theta ={45}^{\circ }$

Hence, the correct answer is option (b).