How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8})$ $cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8})$ $cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-13T09:08:14

$\frac{1}{2} + \frac{1}{2} cos (\frac{π}{4})$ $1/2+1/2cos(pi/4)$

Explanation:

$cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8}) = {cos}^{2} (\frac{15 π}{8})$ $cos((15pi)/8)*cos((15pi)/8)=cos^2((15pi)/8)$

As $cos 2 A = 2 {cos}^{2} A - 1$ $cos2A=2cos^2A-1$ , ${cos}^{2} A = \frac{1}{2} + \frac{cos 2 A}{2}$ $cos^2A=1/2+(cos2A)/2$

Hence $cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8}) = \frac{1}{2} + \frac{1}{2} cos (\frac{15 π}{4})$ $cos((15pi)/8)*cos((15pi)/8)=1/2+1/2cos((15pi)/4)$

= $\frac{1}{2} + \frac{1}{2} cos (4 π - \frac{π}{4})$ $1/2+1/2cos(4pi-pi/4)$

= $\frac{1}{2} + \frac{1}{2} cos (- \frac{π}{4}) = \frac{1}{2} + \frac{1}{2} cos (\frac{π}{4})$ $1/2+1/2cos(-pi/4)=1/2+1/2cos(pi/4)$

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8})$ $cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )$ without using products of trigonometric functions?

1 Answer

Explanation:

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How do you express cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 ) cos(15π8)⋅cos(15π8)cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 ) without using products of trigonometric functions?

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Explanation:

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{15 π}{8})$ $cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )$ without using products of trigonometric functions?