Question

Given that sin θ = `a/b`, then cos θ is equal to ______.

पर्याय

• `b/sqrt(b^2 - a^2)`

• `b/a`

• `sqrt(b^2 - a^2)/b`

• `a/sqrt(b^2 - a^2)`

Answer 1

Given that sin θ = `a/b`, then cos θ is equal to `underlinebb(sqrt(b^2 - a^2)/b)`.

Explanation:

According to the question,

sin θ = `a/b`

We know,

sin²θ + cos²θ = 1

sin²A = 1 – cos²A

sin A = `sqrt(1 - cos^2A)`

So, cos θ = `sqrt(1 - a^2/b^2)`

= `sqrt((b^2 - a^2)/b^2)`

= `sqrt(b^2 - a^2)/b`

Hence, cos θ = `sqrt(b^2 - a^2)/b`