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Question

If 3cosx+2cos3x=cosy,3sinx+2sin3x=siny, then the value of cos2x is

A
1
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B
1
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C
0
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D
12
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Solution

The correct option is A 1
3cosx+2cos3x=cosy

Squaring

9cos2x+4cos23x+12cosxcos3x=cos2y ...(1)

3sinx+2sin3x=siny

Squaring

9sin2x+4sin23x+12sinxsin3x=sin2y ...(2)

Adding (1) and (2)

9(cos2x+sin2x)+4(cos23x+sin23x)+12(cosxcos3x+sinxsin3x)=cos2y+sin2y

9+4+12cos(3xx)=1

12cos(2x)=12

cos2x=1


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