Express the following as a single trignometric ratio:
`sqrt3 costheta-sintheta`
`sintheta-costheta`.

Explanation

(a) Given, `sqrt3costheta-sintheta=2((sqrt3)/(2)costheta-(1)/(2)sintheta)`
`2(costheta*cos30^(@)-sintheta*sin30^(@))=2(cos(theta+30^(@)))`
`rArrsqrt3costheta-sintheta=2cos(theta+30^(@))`.
(b) ` sintheta-costheta=sqrt2((sintheta-costheta)/(sqrt2))`
`=sqrt2((1)/(sqrt2)sintheta-(1)/(sqrt2)costheta)=sqrt2[sinthetacos((pi)/(4))-costhetasin((pi)/(4))]`
`sqrt2sin(theta-(pi)/(4)) " " [therefore sin (A-B)=sin A cos B -cos A sin B]`