Question

If (tan θ + 2) (2tan θ + 1) = A tan θ + B sec²θ, then AB = _________.

Answer 1

$$\begin{gathered} \left(\tan \theta +2\right)\left(2\tan \theta +1\right) \\ =2{\tan }^2\theta +\tan \theta +4\tan \theta +2 \\ =2\left({\tan }^2\theta +1\right)+5\tan \theta \\ =2{\sec }^2\theta +5\tan \theta \left(1+{\tan }^2\theta ={\sec }^2\theta \right) \end{gathered}$$

Comparing with the given expression, we get

A = 5 and B = 2

∴ AB = 5 × 2 = 10

If (tan θ + 2) (2tan θ + 1) = A tan θ + B sec²θ, then AB = ____10____.