Express 2 cos x – sin x in the form Rcos( x + a ), where R and a are constants, R > 0 and a is between 0 and 90 ° Give the exact value of R and give the value of to 2 decimal places.
2cosx - sinx = Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a)
Implying
2cos(x)=Rcos(x)cos(a)
Rcosa = 2
Similarly: Rsin(a) = 1
Therefore tan(a) = 1/2
Meaning a=26.57 Degrees
R2(sin2a+cos2a)=5
Implying, given sin2a+cos2a=1, R= Root(5)
Answer 2cosx-sinx=(Root5)(cos[x+26.57])
TO
