10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

If \[(\tan \theta +2)(2\tan \theta +1)=A\tan \theta +B{{\sec }^{2}}\theta ,\] then AB is:

A) \[0\]

B) \[1\]

C) \[-1\]

D) \[10\]

Correct Answer: D

Solution :

[d]\[(\tan \theta +2)(2\tan \theta +1)=2{{\tan }^{2}}\theta +5\tan \theta +2\]

\[=2({{\sec }^{2}}\theta -1)+5\tan \theta +2\]

\[=5\tan \theta +2{{\sec }^{2}}\theta =A\tan \theta +B{{\sec }^{2}}\theta \]

On comparing, we get

\[A=5\] and \[B=2\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,AB=5\times 2=10\]