Reduce each of the following expressions to the sine and cosine of a single expression: `sintheta-costheta`

Explanation

Suppose `f(theta) = sin theta – cos theta`

On dividing and multiplying by `sqrt((1)^2 + 1^2)` i.e. by 2


`f(theta) = sqrt(2)(1/sqrt(2) sin theta – 1/sqrt(2) cos theta)`

f(theta) = `sqrt(2)(cos (pi/4) cos theta – sin (pi/4)sintheta) `

As we know that `cosAcosB–sinAsinB=cos(A+B)`

=`sqrt(2)cos(pi/4+theta)`