what does the expression cos 40°cos10°+sin40°sin10° equal?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the value of : (cos 40)(cos 10) + (sin 40)(sin 10).

cos (a - b) = (cos a)(cos b) + (sin a)(sin b)

(cos 40)(cos 10) + (sin 40)(sin 10)

=> cos (40 - 10)

=> cos 30

=> (sqrt 3)/2

The expression (cos 40)(cos 10) + (sin 40)(sin 10) = (sqrt 3)/2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll recognize the identity:

cos(x-y)=cos x*cos y + sin x*sin y

Let x = 40 and y = 10

The given sum could be written:

cos 40*cos 10 + sin 40*sin 10 = cos (40 - 10)

cos 40*cos 10 + sin 40*sin 10 = cos 30

But cos 30 = (sqrt 3)/2

The given sum is equal to: cos 40*cos 10 + sin 40*sin 10 = (sqrt 3)/2.

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