Question

Sin + coseIf tan0 = 1 then, find the values ofsec 0 + cosec​

Answer 1

Answer:

We know that:

Tan(x) = sin(x)/cos(x)

We know that:

Tan(θ) = 1 = sin(θ)/cos(θ)

we can rewrite this as:

sin(θ)/cos(θ) = 1

sin(θ) = cos(θ)

If you know the table of notable angles, the angle such that this is true is θ = 45°

sin(45°) = 1/√2 = cos(45°)

Now we want to find the value of:

sec(θ) + cosec(θ)

Where:

sec(θ) = 1/cos(θ)

cosec(θ) = 1/sin(θ)

And we already know the values of the sine and cosine function, then:

sec(45°) + cosec(45°) = 1/cos(45°) + 1/sin(45°) = 2*(1/( 1/√2)) = 2*√2

Then, given that:

Tan(θ) = 1

We can conclude that:

sec(θ) + cosec(θ) = 2*√2