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

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

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Answer 1 · 2016-03-03T22:50:47

It is $cos(15pi/8)*cos(pi/3)=1/2[cos(5*pi/24)+cos(37/24*pi)]$

Explanation:

Well we know that

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

and

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

Add these two to get

$cosA*cosB=1/2[cos(A+B)+cos(A-B)]$

Hence for $A=15pi/8$ and $B=pi/3$ 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 $cos( (15 pi)/ 8 ) * cos (( pi) /3 )$ without using products of trigonometric functions?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

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