SOLUTION: assuming that cos(alpha)=-6/7 with alpha between pi/2 and pi and that cos(beta)=8/9 with beta between 3pi/2 and 2pi, evaluate cos(alpha+beta) exactly.
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Question 1052903: assuming that cos(alpha)=-6/7 with alpha between pi/2 and pi and that cos(beta)=8/9 with beta between 3pi/2 and 2pi, evaluate cos(alpha+beta) exactly.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{36}{49})
\ =\ \frac{36}{49})
\ =\ \frac{13}{49})
\ =\ \pm\frac{\sqrt{13}}{7})
But 
is positive in QII, so
\ =\ \frac{\sqrt{13}}{7})
Similarly
\ =\ -\frac{\sqrt{17}}{9})
\ =\ \cos(\alpha)\cos(\beta)\ -\ \sin(\alpha)\sin(\beta))
So:
\ =\ \left(-\frac{6}{7}\right)\left(\frac{8}{9}\right)\ -\ \left(\frac{\sqrt{13}}{7}\right)\left(-\frac{\sqrt{17}}{9}\right))
I'll leave it to you to simplify.
John
My calculator said it, I believe it, that settles it
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