Express 8cos²x - 6sin x cos x + 2 as rcos(2x+α) + s

[kingboy]

Homework Statement

show that the expression 8 cos^2 x -6 sin x cos x +2 may be expressed in the form rcos (2x+α)+s ,and determine the value of the constants r,s and α.hence ,or otherwise, find the greatest and latest values of the expression as x varies.

Homework Equations

cos 2x=cos^2x-sin^2x ,sin2a=2 sinxcosx ,acos x-bsinx=rcos(x+α)

The Attempt at a Solution

8 cos^2 x -6 sin x cos x +2=8(cos 2x+sin^2x)+3(2 sinxcosx)+2=?

 

[tiny-tim]

hi kingboy!

(try using the X² icon just above the Reply box )

cos 2x=cos^2x-sin^2x

learn all your trignonmetric identiies …

in this case, more useful would be cos2x = 2cos²x - 1

 

[suwarna07]

in this case, more useful would be cos2x = 2cos²x - 1

agreed :D