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Question

The value of α satisfying 6sin2α5cosα=2 is

A
α=π2
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B
α=π3
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C
α=π4
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D
α=π6
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Solution

The correct option is C α=π3

Consider the given equation,

6sin2α5cosα=2

6(1cos2α)5cosα=2

66cos2α5cosα2=0

6cos2α5cosα+4=0

6cos2α+5cosα4=0

6cos2α+8cosα3cosα4=0

2cosα(3cosα+2)1(3cosα+2)=0

(3cosα+2)(2cosα1)=0

When,

3cosα+2=0

cosα=23

α=cos1(23)

When,

2cosα1=0

cosα=12

cosα=cosπ3

α=π3

Hence, this is the answer.


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