Question

If (tan θ + 2) (2 tan θ + 1) = A tan θ + B sec² θ, then AB = ______.

Answer 1

If (tan θ + 2) (2 tan θ + 1) = A tan θ + B sec² θ, then AB = 10.

Explanation:

Expand the left side: (tan θ + 2)(2 tan θ + 1) = 2 tan² θ + 5 tan θ + 2.

Write the right side using sec² θ = 1 + tan² θ.

A tan θ + B sec² θ = A tan θ + B(1 + tan² θ)

= B tan² θ + A tan θ + B

Equate coefficients: tan²: B = 2 tan: A = 5 

Thus AB = 5 × 2 = 10.