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Express Cosx-3Sinx in form Rcos(x+a) and show that cosx-3sinx=4 has no solution MEI OCR June 2016 C4

Cosx-3sinx =R(CosxCosa-SinxSina) 1=Rcosa R^2=1^2+3^2 r=(10)^0.5=(approx)3.16 a=1.249 3.16Cos(x+1.249)=4 has no solution as 4<3.16 so as cos(theta) has maximum value of 1, there are no solutions

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Express Cosx-3Sinx in form Rcos(x+a) and show that cosx-3sinx=4 has no solution MEI OCR June 2016 C4

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