InterviewSolution
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InterviewSolution
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Solve the equation `sqrt3cos x + sin x = sqrt2 `. |
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Answer» We have, `sqrt(3) cos x + sin x=sqrt(2)` ...(1) Dividing both sides by `sqrt((sqrt(3))^(2)+1^(2))=2`, we get `sqrt(3)/2 cos x+1/2 sin x=1/sqrt(2)` `rArr cos(x-pi/6)=1/sqrt(2)` `rArr cos(x-pi/6)="cos" pi/4` `rArr x-pi/6=2n pi pm pi/4, n in Z` `rArr x= 2n pi pm pi/4+pi/6` `rArr x=2npi +pi/4+pi/6 or x=2npi - pi/4+pi/6` `rArr x=2n pi +(5 pi)/12 or x=2npi-pi/12`, where `n in Z` |
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