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Question

If cos2α=(3cos2β-1)(3-cos2β), then tanαis equal to


A

2tanβ

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B

tanβ

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C

sin2β

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D

2cotβ

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Solution

The correct option is A

2tanβ


Explanation for the correct option:
Finding the value of tanα:

Given

cos2α=(3cos2β1)(3cos2β).(i)tan2α=(sin2α)(cos2α)=(2sin2α)(2cos2α)=(1cos2α)(1+cos2α)

Substituting in equation 1

tan2α=[1(3cos2β1)(3cos2β][1+(3cos2β1)(3cos2β]=(3cos2β3cos2β+1)(3cos2β+3cos2β1)=(44cos2β)(2+2cos2β)=2(1cos2β)(1+cos2β)=2(2sin2β)(2cos2β)=2tan2β

tanα=2tanβ

Hence, Option ‘A’ is Correct.


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