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Question
If sin A = `1/2`, then the value of cot A is ______.
Options
`sqrt(3)`
`1/sqrt(3)`
`sqrt(3)/2`
1
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Solution
If sin A = `1/2`, then the value of cot A is `underlinebb(sqrt(3))`.
Explanation:
According to the question,
sin A = `1/2` ...(1)
We know that,
cot A = `1/(tan A) = (cos A)/(sin A)` ...(2)
To find the value of cos A.
We have the equation,
sin2 θ + cos2 θ = 1
So, cos θ = `sqrt(1 - sin^2θ)`
Then,
cos A = `sqrt(1 - sin^2A)` ...(3)
cos2A = 1 – sin2A
cos A = `sqrt(1 - sin^2A)`
Substituting equation 1 in 3, we get,
cos A = `sqrt(1 - 1/4)`
= `sqrt(3/4)`
= `sqrt(3)/2`
Substituting values of sin A and cos A in equation 2, we get
cot A = `(sqrt(3)/2) xx 2`
= `sqrt(3)`
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