Question 50

What is the value of cos 15° - cos 165°?

Solution

cos 15 = cos (45-30)

=> cos 15 = cos 45 * cos 30 + sin 45 * sin 30

=> cos 15 = (1/√2)* (√3/2) + (1/√2)*(1/2)

=> cos 15 = (√3 + 1 )/2√2

$$\cos15^{\circ\ }-\cos165^{\circ\ }=\cos15^{\circ\ }+\cos15^{\circ\ }=2\cos15^{\circ\ }.$$

So,

$$\cos15^{\circ\ }-\cos165^{\circ\ }=\frac{\sqrt{3}+1}{\sqrt{2}}\ .$$

C is correct choice.

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