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, sin² θ + cos² θ = 1

sin² A = 1 – cos² A

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

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"`