Question

Use the sum to product formula to find exact values: if cos255 - cos195 = squrtroot a/ 2 then a=

Answer 1

By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

How to analyze a trigonometric expression

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

$\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)$

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

To learn more on trigonometric expressions: brainly.com/question/10083069

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