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Cos75Cos15-sin75sin15

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kaiteo96 | eNotes Newbie

Posted March 31, 2013 at 12:53 AM via iOS

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Cos75Cos15-sin75sin15

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted March 31, 2013 at 1:20 AM (Answer #2)

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Im not sure about your question here. If you need to simplify, you can just use your calculator and input cos(75)cos(15)-sin(75)sin(15) and press =.

You will be getting zero (0).

There is and identity for `cos(75)cos(15)-sin(75)sin(15)` .

Recall `cos(A+B) = cosAcosB - sinAsinB.`

Simply, A = 75 and B = 15.

So cos(75+15) = cos(90) = 0.

Therefore, the answer is 0.

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted March 31, 2013 at 8:34 AM (Answer #3)

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We know that cosAcosB-sinAsinB=cos(A+B)

cos75.cos15-sin75.sin15=cos(75+15)

                                    =cos90  (If The angle given is in degree)

                                   =0

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jaderade | Student, Grade 11 | eNotes Newbie

Posted March 31, 2013 at 1:16 AM (Answer #1)

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note:

cos(x)*cos(y) = 1/2 (cos(x-y)+cos(x+y))
and
sin(x)sin(y) = 1/2 (cos(x-y)-cos(x+y))

therefor: 1/2 (cos(x-y)-cos(x+y)) - 1/2 (cos(x-y)-cos(x+y)) = 0

if you punch it into a calculator you get:

=(1/4)-(1/4)

=0

Sources:

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