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ques 16

Asked by rbhatt16 12th December 2017, 4:21 PM
Answered by Expert
Answer:
begin mathsize 16px style Let space straight pi 3 to the power of straight x equals straight z
Then space question space will space be
cosz minus 2 cos squared straight z plus 2 cos 4 straight z minus cos 7 straight z equals sinz plus 2 sin squared straight z minus 2 sin 4 straight z plus 2 sin 3 straight z minus sin 7 straight z
cosz minus cos 7 straight z minus sinz plus sin 7 straight z equals 2 sin squared straight z minus 2 sin 4 straight z plus 2 sin 3 straight z plus 2 cos squared straight z minus 2 cos 4 straight z
2 sin 4 zsin 3 straight z plus 2 cos 4 zsin 3 straight z equals 2 open parentheses sin squared straight z plus cos squared straight z close parentheses minus 2 sin 4 straight z plus 2 sin 3 straight z minus 2 cos 4 straight z
sin 4 zsin 3 straight z plus cos 4 zsin 3 straight z equals 1 minus sin 4 straight z plus sin 3 straight z minus cos 4 straight z
sin 4 straight z left parenthesis 1 plus sin 3 straight z right parenthesis plus sin 3 straight z left parenthesis cos 4 straight z minus 1 right parenthesis equals 1 minus cos 4 straight z
sin 4 straight z left parenthesis 1 plus sin 3 straight z right parenthesis equals open parentheses 1 minus cos 4 straight z close parentheses plus sin 3 straight z open parentheses 1 minus cos 4 straight z close parentheses
sin 4 straight z left parenthesis 1 plus sin 3 straight z right parenthesis equals open parentheses 1 minus cos 4 straight z close parentheses open parentheses 1 plus sin 3 straight z close parentheses
sin 4 straight z left parenthesis 1 plus sin 3 straight z right parenthesis minus open parentheses 1 minus cos 4 straight z close parentheses open parentheses 1 plus sin 3 straight z close parentheses equals 0
left parenthesis 1 plus sin 3 straight z right parenthesis open parentheses sin 4 straight z minus 1 plus cos 4 straight z close parentheses equals 0
1 plus sin 3 straight z equals 0 space space space space space OR space space space space space sin 4 straight z minus 1 plus cos 4 straight z equals 0
sin 3 straight z equals negative 1 space space space space space space space space OR space space space space sin 4 straight z plus cos 4 straight z equals 1
Consider comma
sin 4 straight z plus cos 4 straight z equals 1
open parentheses sin 4 straight z plus cos 4 straight z close parentheses squared equals 1
Solving space this space you space get space sin 8 straight z equals 0
Putting space straight z equals straight pi 3 to the power of straight x
Find space value space of space straight x.
end style
Answered by Expert 22nd December 2017, 1:07 PM
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