Write the expression as a function of $θ$ , with no angle measure involved.
$\cos (45^{\circ} - θ)$
$\cos (45^{\circ} - θ) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

$\cos (45^{\circ} - θ) = \frac{\sqrt{2}}{2} (\cos θ + \sin θ)$ is the final answer.

Steps

Step 1 ：We know that $\cos (a - b) = \cos a \cos b + \sin a \sin b$ .

Step 2 ：Substitute $a = 45^{\circ}$ and $b = θ$ into the formula, we get $\cos (45^{\circ} - θ) = \cos 45^{\circ} \cos θ + \sin 45^{\circ} \sin θ$ .

Step 3 ：From the solution of QuestionA, we know that $\cos 45^{\circ} = \frac{\sqrt{2}}{2}$ and $\sin 45^{\circ} = \frac{\sqrt{2}}{2}$ .

Step 4 ：Substitute $\cos 45^{\circ} = \frac{\sqrt{2}}{2}$ and $\sin 45^{\circ} = \frac{\sqrt{2}}{2}$ into the formula, we get $\cos (45^{\circ} - θ) = \frac{\sqrt{2}}{2} \cos θ + \frac{\sqrt{2}}{2} \sin θ$ .

Step 5 ：Factor out $\frac{\sqrt{2}}{2}$ , we get $\cos (45^{\circ} - θ) = \frac{\sqrt{2}}{2} (\cos θ + \sin θ)$ .

Step 6 ： $\cos (45^{\circ} - θ) = \frac{\sqrt{2}}{2} (\cos θ + \sin θ)$ is the final answer.

Write the expression as a function of θ, with no angle measure involved.cos⁡(45∘−θ)cos⁡(45∘−θ)=(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

Popular Problems

Write the expression as a function of $θ$ , with no angle measure involved.
$\cos (45^{\circ} - θ)$
$\cos (45^{\circ} - θ) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)