Question

write the expression as a function of θ, with no angle measure involved. cos (60° - θ) cos (60° - θ) = □ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Use the cosine subtraction formula

The formula for \(\cos(A - B)=\cos A\cos B+\sin A\sin B\). Here \(A = 60^{\circ}\) and \(B=\theta\). So \(\cos(60^{\circ}-\theta)=\cos60^{\circ}\cos\theta+\sin60^{\circ}\sin\theta\).

Step2: Substitute the values of \(\cos60^{\circ}\) and \(\sin60^{\circ}\)

We know that \(\cos60^{\circ}=\frac{1}{2}\) and \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\). Substituting these values, we get \(\cos(60^{\circ}-\theta)=\frac{1}{2}\cos\theta+\frac{\sqrt{3}}{2}\sin\theta\).

Answer:

\(\frac{1}{2}\cos\theta+\frac{\sqrt{3}}{2}\sin\theta\)