If cos θ = 2/3, write the value of (4 +4 tan2 θ).
Give: cos θ = 2/3
Therefore sec θ = 1/cos θ
= 3/2
Consider 4 tan2 θ + 4 = 4 (tan2 θ + 1)
= 4 sec2 θ (∵ 1 + tan2 θ = sec2 θ)
= 4 (3/2)2
= 4 × (9/4)
= 9