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Question

Find all values between 0 and π which satisfies the equation : sin8c+cos8x=1716cos22x

A
x=nπ2±(1)nπ8;nϵz
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B
x=nπ2+(1)nπ8;nϵz
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C
x=nπ2(1)nπ8;nϵz
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D
x=nπ4±(1)nπ8;nϵz
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Solution

The correct option is A x=nπ2±(1)nπ8;nϵz
sin8x+cos8x=1732
(sin4x+cos4x)22sin4xcos4x=1732
(12sin2xcos2x)22sin4xcos4x=1732
14sin2xcos2x+2sin4xcos4x=1732
1(2sinxcosx)2+18(2sinxcosx)41732
1sin2x+18sin42x1732=04sin42x32sin22x+15=0
2sin22x1=0[sin22x152]
sin22x=122x=nπ±π4x=nπ2±π8

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