Question

If tan 0 = 2, then find sec 0

Answer 1

sec 0 = ±√5

Explanation:

`sec^2\theta - tan^2\theta = 1\\sec^2\theta = 1 + tan^2\theta\\tan\theta = 2\\tan^2\theta = 4\\1 + tan^2\theta = 5\\sec^2\theta = 5\\(√(sec^2\theta) )/(√(1 + tan^2\theta) ) = \pm√(5)`

Negative 5 and positive 5 both work for this equation.

Answer 2

Given:

tan Θ = 2

To FinD:

sec Θ ?

Explanation:

Here we have two types of trigonometric ratios: tan Θ and sec Θ. We know about their relation:

sec² Θ - tan² Θ = 1

Or

sec² Θ = 1 + tan² Θ

So, let's find arrange the given to get the value of sec Θ:

➛ tan Θ = 2

Squaring both sides,

➛ tan² Θ = 4

Adding one to both sides of the eq.

➛ 1 + tan² Θ = 5

➛ sec² Θ = 5

Square-rooting both sides,

➛ sec Θ = ± √5