in the following problem, the expression is the right side of the formula for $\\cos(\\alpha - \\beta)$ with…

in the following problem, the expression is the right side of the formula for $\\cos(\\alpha - \\beta)$ with particular values for $\\alpha$ and $\\beta$.\n$\\cos(62^{\\circ})\\cos(32^{\\circ})+\\sin(62^{\\circ})\\sin(32^{\\circ})$\n\n a. identify $\\alpha$ and $\\beta$ in each expression.\n the value for $\\alpha$: $62^{\\circ}$\n the value for $\\beta$: $32^{\\circ}$\n b. write the expression as the cosine of an angle. $\\cos 30^{\\circ}$\n c. find the exact value of the expression.\n (type an exact answer, using fraction, radicals and a rationalized denominator.)

in the following problem, the expression is the right side of the formula for $\\cos(\\alpha - \\beta)$ with particular values for $\\alpha$ and $\\beta$.\n$\\cos(62^{\\circ})\\cos(32^{\\circ})+\\sin(62^{\\circ})\\sin(32^{\\circ})$\n\n a. identify $\\alpha$ and $\\beta$ in each expression.\n the value for $\\alpha$: $62^{\\circ}$\n the value for $\\beta$: $32^{\\circ}$\n b. write the expression as the cosine of an angle. $\\cos 30^{\\circ}$\n c. find the exact value of the expression.\n (type an exact answer, using fraction, radicals and a rationalized denominator.)

Answer

Explanation:

Step1: Use the cosine difference formula

The formula for (\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta). From part (b), we know the expression is (\cos(62^{\circ} - 32^{\circ})=\cos30^{\circ}).

Step2: Find the value of (\cos30^{\circ})

We know that (\cos30^{\circ}=\frac{\sqrt{3}}{2})

Answer:

(\frac{\sqrt{3}}{2})