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find the exact value of cos(8deg)cos(38deg)+sin(8deg)sin(38deg) 

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ssdixon | Student, Undergraduate | (Level 1) Salutatorian

Posted May 6, 2012 at 5:20 AM via web

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find the exact value of cos(8deg)cos(38deg)+sin(8deg)sin(38deg) 

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beckden | High School Teacher | (Level 1) Educator

Posted May 6, 2012 at 5:40 AM (Answer #1)

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We know `cos(A-B)=cos(A)cos(B)+sin(A)sin(B)` so

`cos(8^o)cos(38^o)+sin(8^o)sin(38^o) = cos(38^o-8^o) = cos(30^o) = sqrt(3)/2`

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malagala | College Teacher | (Level 2) Adjunct Educator

Posted May 6, 2012 at 5:49 AM (Answer #2)

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For this question we can use the following equation,

cos(A-B) = cos(A)cos(B) + sin(A)sin(B)

In this example we can use,

A = 8 deg and B= 38 deg

hence we can write the equation as,

cos(8)cos(38) + sin(8)sin(38)

=> cos(8-38)

=> cos(-30) ----> as cos(-D) = cos(D)

=> cos(30)

=>(3^(1/2))/2 = (sqrt(3))/2

 

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