`cos(pi/16)cos((3pi)/16) - sin(pi/16)sin((3pi)/16)` Find the exact value of the expression.

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It is in the form of `cos A cos B - sin A sin B`  

That is equal to 

from the question, we get `A = pi/16` and `B = (3pi)/16`

 

`therefore cos(A+B) = cos[pi/16 + (3pi)/16] `

 `=cos[(4pi)/16] = cos (pi/16) `

  `= 1/sqrt2`

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You need to evaluate the expression using the formula `cos a*cos b - sin a*sin b = cos (a + b)` . You need to put `a = pi/16` and `b = (3pi)/16,` such that:

`cos (pi/16)*cos ((3pi)/16) - sin (pi/16) *sin ((3pi)/16) = cos (pi/16 + (3pi)/16)`

`cos (pi/16)*cos ((3pi)/16) - sin (pi/16) *sin ((3pi)/16) = cos ((4pi)/16)`

`cos (pi/16)*cos ((3pi)/16) - sin (pi/16) *sin ((3pi)/16) = cos (pi/4) = sqrt2/2`

Hence, evaluating the given expression yields that it is the cosine of the sum of the angles `a = pi/16` and `b = (3pi)/16` , such that `cos (pi/16)*cos ((3pi)/16) - sin (pi/16) *sin ((3pi)/16) = cos (pi/4) = sqrt2/2.`

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