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Find the value of a specific angle Calculate cos 165

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cos 165 = cos(180 - 15) = -cos 15

We use the value of cos 30 to find cos 15. The relation cos...

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giorgiana1976 | Student

We'll write 165 as sum of 2 angles: 90 and 75.

cos(165) = cos (90 + 75)

We'll use the identity:

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

Comparing, we'll get:

cos (90 + 75) = cos 90*cos 75 - sin 90*sin 75

We'll substitute cos 90 = 0 and sin 90 = 1

cos (90 + 75) = -sin 75

We'll write 75 as a sum of 2 known angles: 30+45

sin 75 = sin(30+45)

sin(30+45) = sin30*cos45 + sin45*cos30

sin(30+45) = (sqrt2)*(1+sqrt3)/4

cos(165) = -sin 75

The value of cos(165) = -(sqrt2)*(1+sqrt3)/4

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