How do i find the exact value for
(Cos 5pi/16)(Cos pi/16) + (sin 5pi/16)(sin pi/16)
well, cos(A-B) = cosAcosB + sinAsinB
To find the exact value for the expression (cos 5π/16)(cos π/16) + (sin 5π/16)(sin π/16), we can make use of a trigonometric identity called the cosine addition formula. The cosine addition formula states that:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
We can rewrite the given expression as follows:
(cos 5π/16)(cos π/16) + (sin 5π/16)(sin π/16) = cos(5π/16 + π/16)
Using the cosine addition formula, we have:
cos(5π/16 + π/16) = cos(6π/16) = cos(3π/8)
Now, to find the exact value of cos(3π/8), we need to refer to the unit circle or use a calculator. The value of cos(3π/8) is approximately 0.3827.
Therefore, the exact value of the given expression is approximately 0.3827.