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

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

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Answer 1 · 2016-03-03T22:50:47

It is $cos (15 \frac{π}{8}) \cdot cos (\frac{π}{3}) = \frac{1}{2} [cos (5 \cdot \frac{π}{24}) + cos (\frac{37}{24} \cdot π)]$ $cos(15pi/8)*cos(pi/3)=1/2[cos(5*pi/24)+cos(37/24*pi)]$

Explanation:

Well we know that

$cos (A + B) = cos A \cdot cos B - sin A \cdot sin B$ $cos(A+B)=cosA*cosB-sinA*sinB$

and

$cos (A - B) = cos A \cdot cos B + sin A \cdot sin B$ $cos(A-B)=cosA*cosB+sinA*sinB$

Add these two to get

$cos A \cdot cos B = \frac{1}{2} [cos (A + B) + cos (A - B)]$ $cosA*cosB=1/2[cos(A+B)+cos(A-B)]$

Hence for $A = 15 \frac{π}{8}$ $A=15pi/8$ and $B = \frac{π}{3}$ $B=pi/3$ we have that

$cos(15pi/8)*cos(pi/3)=1/2[cos(15pi/8+pi/3)+cos(15pi/8-pi/3)]=> cos(15pi/8)*cos(pi/3)=1/2[cos(53/24*pi)+cos(37/24*pi)]=> cos(15pi/8)*cos(pi/3)=1/2[cos(5*pi/24)+cos(37/24*pi)]$

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

1 Answer

Explanation:

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

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