Question

If tan θ = `x/y`, then cos θ is equal to ______.

Options

• `x/sqrt(x^2 + y^2)`

• `y/sqrt(x^2 + y^2)`

• `x/sqrt(x^2 - y^2)`

• `y/sqrt(x^2 - y^2)`

Answer 1

If tan θ = `x/y`, then cos θ is equal to `underlinebb(y/sqrt(x^2 + y^2))`.

Explanation:

Given, tan θ = `x/y`   ...(i)

We know that

tan θ = `"Perpendicular (P)"/"Base (B)"`  ...(ii)

By comparing equations (i) and (ii), we get

P = x, B = y

H² = P² + B²   ...(Pythagoras theorem)

H² = x² + y² 

H = `sqrt(x^2 + y^2)`

Then cos θ = `B/H`

= `y/sqrt(x^2 + y^2)`