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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)`
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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,
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`
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