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Question
Select the correct option from the given alternatives :
If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to
Options
`(1 + n)/(2 - n) tan alpha`
`(1 - n)/(1 + n) tan alpha`
tan α
`(1 + n)/(1 - n) tan alpha`
Solution
`(1 + n)/(1 - n) tan alpha`
Explanation:
`(sin(theta + 2alpha))/sintheta = 1/n`
∴ `(sin(theta + 2alpha) + sintheta)/(sin(theta + 2alpha) - sintheta) = (1 + n)/(1 - n)`
∴ `(2sin(theta + alpha)cos alpha)/(2cos(theta + alpha)sin alpha) =(1 + n)/(1 - n)`
∴ `tan (theta + alpha) = (1 + n)/(1 - n) tan alpha`
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