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Find the exact value, Sum and Difference Identities

Can someone explain how to solve this type of problem? Ik you hv to find something on the unit circle but im not sure what..

Find the exact value, Sum and Difference Identities Can someone explain how to solve-example-1

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The exact value of the cos (17π / 12) is determined as (√2 - √6)/4

How to calculate the exact value of cos function?

The exact value of the cosine function is calculated by applying the following as shown below.

The given cosine function is

cos (17π / 12)

The function is simplified as follows;

π = 180⁰

17 π / 12 = (17 x 180⁰ ) / 12

17 π / 12 = 255⁰

Cos (255) = cos( 180 - 255)

= - cos(75)

Using trigonometry identity of cos (a + b)

cos (a + b) = cos (a) cos(b) - sin (a) sin(b)

- cos (75) = - [ cos(30 + 45)]

- [ cos(30 + 45)] = - [ cos (30) cos(45) - sin (30) sin(45) ]

- [ cos (30) cos(45) - sin (30) sin(45) ] = - [ √3/2 × √2/2 - ¹/₂ × √2/2]

The expression is simplified further as;

= - [ √3/2 × √2/2 - ¹/₂ × √2/2]

= - [√6/4 - √2/4]

= - √6/4 + √2/4

= (√2 - √6)/4

User Muhammad Saqib
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