How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{5 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 5 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{5 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 5 pi) /3 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-13T07:48:17

$\frac{1}{2} cos (\frac{11 π}{24}) + \frac{1}{2} cos (\frac{5 π}{24})$ $1/2cos((11pi)/24)+1/2cos((5pi)/24)$

Explanation:

As $cos (A + B) = cos A cos B - sin A sin B$ $cos(A+B)=cosAcosB-sinAsinB$ and $cos (A - B) = cos A cos B + sin A sin B$ $cos(A-B)=cosAcosB+sinAsinB$ , adding them gives us

$cos (A + B) + cos (A - B) = 2 cos A cos B$ $cos(A+B)+cos(A-B)=2cosAcosB$

Hence $cos A cos B = \frac{1}{2} {cos (A + B) + cos (A - B)}$ $cosAcosB=1/2{cos(A+B)+cos(A-B)}$ and

$cos (15 \frac{π}{8}) cos (5 \frac{π}{3}) = \frac{1}{2} {cos (\frac{15 π}{8} + \frac{5 π}{3}) + cos (\frac{15 π}{8} - \frac{5 π}{3})}$ $cos(15pi/8)cos(5pi/3)=1/2{cos((15pi)/8+(5pi)/3)+cos((15pi)/8-(5pi)/3)}$

= $\frac{1}{2} {cos (\frac{45 π + 40 π}{24}) + cos (\frac{45 π - 40 π}{24})}$ $1/2{cos((45pi+40pi)/24)+cos((45pi-40pi)/24)}$

= $\frac{1}{2} {cos (\frac{85 π}{24}) + cos (\frac{5 π}{24})}$ $1/2{cos((85pi)/24)+cos((5pi)/24)}$

= $\frac{1}{2} {cos (\frac{96 π - 11 π}{24}) + cos (\frac{5 π}{24})}$ $1/2{cos((96pi-11pi)/24)+cos((5pi)/24)}$

= $\frac{1}{2} {cos (4 π - \frac{11 π}{24}) + cos (\frac{5 π}{24})}$ $1/2{cos(4pi-(11pi)/24)+cos((5pi)/24)}$

= $\frac{1}{2} cos (\frac{11 π}{24}) + \frac{1}{2} cos (\frac{5 π}{24})}$ $1/2cos((11pi)/24)+1/2cos((5pi)/24)}$

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{5 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 5 pi) /3 )$ without using products of trigonometric functions?

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Explanation:

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How do you express cos(15π8)⋅cos(5π3)cos( (15 pi)/ 8 ) * cos (( 5 pi) /3 ) without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{5 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 5 pi) /3 )$ without using products of trigonometric functions?