Question

If cos θ = 2/3 then 2 sec²θ + 2tan²θ – 4 is equal to
A. 1
B. 0
C. 3
D. 4

Answer 1

C. 3

Step-by-step explanation:

Given: cos θ = 2/3

So 2 sec²θ + 2tan²θ – 4 = 2(1/sin²θ) + 2(sin²θ/cos²θ) - 4

= 2 (1 / 1-cos²θ) + 2 (1-cos²θ/ cos²θ) - 4

= 2 (1 / (2/3)²) + 2 (1-(2/3)² / (2/3)²) - 4

= 2*9/4 + 2 (5/9) / (4/9) - 4

= 9/2 + 2*5/4 - 4

= 9/2 + 5/2 - 4

= 7 -4

= 3

Option C is the answer.