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Select the correct option from the given alternatives : If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to

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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`

MCQ
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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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Chapter 3: Trigonometry - 2 - Miscellaneous Exercise 3 [Page 56]

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