Question

(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec²θ.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

L.H.S = (tan θ + 2)(2 tan θ + 1)

= 2 tan² θ + tan θ + 4 tan θ + 2

= 2 tan²θ + 5 tan θ + 2

Since, sec²θ – tan²θ = 1, we get, tan²θ = sec²θ – 1

= 2(sec²θ – 1) + 5 tan θ + 2

= 2 sec²θ – 2 + 5 tan θ + 2

= 5 tan θ + 2 sec² θ ≠ R.H.S

∴ L.H.S ≠ R.H.S