Cos(pi/4-L) ришение

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вопрос

To find the value of cos(pi/4 - L), we can use the cosine difference formula:

cos(A - B) = cosAcosB + sinAsinB

In this case, A = pi/4 and B = L. Therefore, we have:

cos(pi/4 - L) = cos(pi/4)cos(L) + sin(pi/4)sin(L)

Using the values of sin(pi/4) = 1/sqrt(2) and cos(pi/4) = 1/sqrt(2), we get:

cos(pi/4 - L) = (1/sqrt(2))cos(L) + (1/sqrt(2))sin(L)

cos(pi/4 - L) = (cos(L) + sin(L))/sqrt(2)

Therefore, the solution to cos(pi/4 - L) is:

(cos(L) + sin(L))/sqrt(2)