Question

Find cos(A+B), given sinA=35 and cosB=−12/13 and both A and B are in π2<θ<π

Answer 1

`\cos(A + B) = \cos A \cos B - \sin A \sin \: B \\ but : \cos \: A = \sqrt{1 - ({ (3)/(5) })^(2) } = (4)/(5) \\ : \sin B = \sqrt{1 - {( ( - 12)/(13) })^(2) } = (5)/(13) \\ \therefore \cos(A + B) = ( (4)/(5) )( ( - 21)/(13) ) - ( (3)/(5) )( (5)/(13) ) \\ = ( - 84)/(65) - (3)/(13) \\ = ( - 99)/(65) \\ = - 1.52`