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Use the product-to-sum identities to rewrite each expression.
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Step by Step Solution:
Step 1. Use the product-to-sum identity: cos(A)cos(B) = 0.5*(cos(A-B)+cos(A+B))
Step 2. Substitute A = pi/6 and B = pi/5
Step 3. cos(pi/6)cos(pi/5) = 0.5*(cos(pi/6-pi/5)+cos(pi/6+pi/5))
Step 4. Simplify the angles inside the cosine functions
Step 5. cos(1/30 pi) = sqrt(3)/2 * sqrt((5 + sqrt(5))/8) and cos(11/30 pi) = sqrt(3)/2 * sqrt((5 - sqrt(5))/8)
Step 6. Substitute the values into the product-to-sum identity in step3
Step 7. cos(pi/6)cos(pi/5) = 0.5*(sqrt(3)/2 * sqrt((5 + sqrt(5))/8) + sqrt(3)/2 * sqrt((5 - sqrt(5))/8))
Step 8. Simplify the expression on the right-hand side of step7
Step 9. cos(pi/6)cos(pi/5) = 1/4 * sqrt(2) * sqrt(10 + 2 * sqrt(5))
Final Answer:
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Question Text | Use the product-to-sum identities to rewrite each expression. |
Topic | All Topics |
Subject | Pre Calculus |
Class | Class 11 |
Answer Type | Text solution:1 |