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Question
Given that sin θ = `a/b` then cos θ is equal to ______.
Options
`b/sqrt(b^2 - a^2)`
`b/a`
`sqrt(b^2 - a^2)/b`
`a/sqrt(b^2 - a^2)`
Solution
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"`
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