In the following problem, the expression is the right side of the formula for co
ID: 3025065 • Letter: I
Question
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta cos (11 pi/12) cos (7 pi/12) + sin (11 pi/12) sin (7 pi/12) a. Identify alpha and beta in the expression. The value of alpha is The value of beta is b. Write the expression as the cosine of an angle. The expression is cos c. Find the exact value of the expression. cos (11 pi/12) cos (7 pi/12) + sin (11 pi/12) sin (7 pi/12) (Type an exact answer, using radicals as needed. Use integers of fractions for any numbers in the expression. Rationalize of denominators. Simplify your answer.)Explanation / Answer
Solution:
By general formula;
cos(a - b) = cos a cos b + sin a sin b
a) by general identity
= 11/12 & = 7/12
b) & c) cos(a - b) = cos a cos b + sin a sin b
cos(11/12 - 7/12) = cos( 11/12) cos( 7/12) + sin( 11/12) sin( 7/12)
=> cos( /3) = cos(60degree) = 1/2
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