SOLUTION: Find the exact values by applying the odd/even identities, cofunction identities, and cosine of sum or difference identities. Do not use a calculator. sin(85�)sin(40�)+sine(-5�)si

Question 759972: Find the exact values by applying the odd/even identities, cofunction identities, and cosine of sum or difference identities. Do not use a calculator.
sin(85�)sin(40�)+sine(-5�)sin(-50�)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact values by applying the odd/even identities, cofunction identities, and cosine of sum or difference identities. Do not use a calculator.
sin(85�)sin(40�)+sine(-5�)sin(-50�)
***
sin85�=cos(90-85)=cos5�
sin40�=cos(90-40)=cos50�
sin(-5�)=-sin5�
sin(-50�)=-sin50�
Identity: cos(s-t)=cos s cos t+sin s sin t
cos(50-5)=cos50�*cos5�+(-sin50�)*(-sin5�)
cos(50-5)=cos45�=√2/2
..
calculator check:
cos50�*cos5�+(-sin50�)*(-sin5�)≈0.6403+0.0667≈0.7071
Exact value=√2/2≈0.7071
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