Question

sum and difference formulas - sine and cosine
express the following as a function of a single angle.
$cos 100^circ cos 28^circ + sin 100^circ sin 28^circ$
sum & difference formulas
sine and cosine
$cos(a pm b) = cos a cos b mp sin a sin b$
$sin(a pm b) = sin a cos b pm cos a sin b$
options: $sin 128^circ$, $cos 128^circ$, $sin 72^circ$, $cos 72^circ$

Explanation:

Step1: Identify the formula

We use the cosine difference formula: $\cos(A - B)=\cos A\cos B+\sin A\sin B$.
Here, $A = 100^{\circ}$ and $B = 28^{\circ}$.

Step2: Apply the formula

Substitute $A = 100^{\circ}$ and $B = 28^{\circ}$ into the formula:
$\cos100^{\circ}\cos28^{\circ}+\sin100^{\circ}\sin28^{\circ}=\cos(100^{\circ}- 28^{\circ})$

Step3: Calculate the angle

Calculate $100^{\circ}-28^{\circ}=72^{\circ}$, so the expression becomes $\cos72^{\circ}$.

Answer:

$\cos 72^{\circ}$ (corresponding to the option: cos 72°)