Find the exact value for cos 165° using the Half-Angle Identity.

Question

Have no clue how to do this.

 

Answer 1

Cos165 = Cos(180-15)

= -Cos15

= -Cos(30/2)

= -sqrt[(1+Cos30)/2]

= - sqrt[1+sqrt(3)/2]/2

= -sqrt[2+sqrt(3)/4]

= -sqrt[2+sqrt(3)]/2

Answer 2

The cos function is negative in second quadrant  and third quadrants.

In second quadrant cos (180 - 15) = - cos(15).

From the Double - Angle formulas, one may generate easily the Half - Angle formulas.

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The exact value of  .