If tan θ + sec θ = 4, then find the value of cos θ ?

Concept:

I. sec² θ – tan² θ = 1

II. a² – b² = (a - b) (a + b)

Calculation:

Given:

tan θ + sec θ = 4     ...(1)

As we know that, sec² θ – tan² θ = 1

⇒ sec² θ – tan² θ = 1

⇒ (sec θ – tan θ) (sec θ + tan θ) = 1

By substituting the value of tan θ + sec θ = 4, in the above equation, we get

⇒ sec θ – tan θ = 1/4     ... (2)

Adding equation (1) and (2), we get

⇒ 2 sec θ = 17/4

⇒ sec θ = 17/8

cos θ = 8/17

Mistake PointsIt is tan θ which is equal to 15/8. The above two equations that we solved were:

tan θ + sec θ = 4

sec θ – tan θ = 1/4