SOLUTION: If sin A=3/5, cos B=8/17, and A and B are acute angles, determine the exact value of tan A tan B

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Question 1175851: If sin A=3/5, cos B=8/17, and A and B are acute angles, determine the exact value of tan A tan B
Found 2 solutions by MathLover1, Solver92311:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


sin+%28A%29=3%2F5+
cos%5E2%28A%29+=+%281+-+sin%5E2%28A%29%29+
cos%5E2%28A%29+=%281+-+%283%2F5%29%5E2%29+
cos%5E2%28A%29+=1+-+9%2F25
cos%5E2%28A%29+=25%2F25-9%2F25
cos%5E2%28A%29+=16%2F25
cos%28A%29+=sqrt%2816%2F25%29
cos%28A%29+=4%2F5
tan+%28A%29=sin+%28A%29%2Fcos%28A%29
tan+%28A%29=+%283%2F5+%29%2F%284%2F5%29
tan+%28A%29=+3%2F4+->the exact value of tan%28A%29

cos+%28B%29=8%2F17+
sin%5E2%28B%29+=+%281+-+cos%5E2%28B%29%29+
sin%5E2%28B%29+=+%281+-+%288%2F17%29%5E2%29+
sin%5E2%28B%29+=+%281+-+64%2F289%29+
sin%5E2%28B%29+=+225%2F289
sin%28B%29+=sqrt%28+225%2F289%29
sin%28B%29+=15%2F17
tan+%28B%29=sin+%28B%29%2Fcos%28B%29
tan+%28B%29=+%2815%2F17%29%2F%288%2F17+%29
tan+%28B%29=+15%2F8 ->the exact value of tan%28B%29

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Use the following identities:





Since the angles are acute, they are in the first quadrant. Both sine and cosine are positive in the first quadrant, hence use the positive roots.



You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it

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