SOLUTION: If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and cot(A + B). Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt

Algebra ->  Trigonometry-basics -> SOLUTION: If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and cot(A + B). Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt      Log On


   

Question 1017539: If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and cot(A + B).
Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt10)/10). I am confused on how to get rid of the square root. Or can i square both sides? Thank you.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
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If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and cot(A + B).
Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt10)/10).
I am confused on how to get rid of the square root. Or can i square both sides? Thank you.
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Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt10)/10).   <----- Mistake


cos A= sqrt%281-sin%5E2%28A%29%29 = sqrt%281+-+%28sqrt%2810%29%2F10%29%5E2%29 = sqrt%281+-+10%2F100%29 = sqrt%28%28100-10%29%2F100%29 = sqrt%2890%2F100%29 = %283%2Asqrt%2810%29%29%2F10     


Notice that the sign of square root was chosen "+" since the angle A is in Q1.

Can you continue and complete it yourself?



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and cot(A + B).
Note: Ok for this question, I used cos A= sqrt(1-sin A^2) and got sqrt((10-sqrt10)/10). I am confused on how to get rid of the square root. Or can i square both sides? Thank you. 
My question is: Why do you need cos A?.

To find tan (A + B) and cot (A + B), you only need: tan A and tan B, since tan+%28A++%2B+B%29+=+%28tan+%28A%29+%2B+tan+%28B%29%29%2F%281+-+tan+%28A%29+tan+%28B%29%29, and cot+%28A+%2B+B%29+=+1%2Fcot+%28A+%2B+B%29

sin+%28A%29+=+sqrt%2810%29%2F10

sin+%28A%29+=+sqrt%2810%29%2F10+=+y%2Fr, so y = sqrt%2810%29, while r = 10

To find x, we get: x%5E2+=+r%5E2+-+y%5E2 ------> x%5E2+=+10%5E2+-+%28sqrt%2810%29%29%5E2 ------> x%5E2+=+100+-+10, or x+=+sqrt%2890%29, or x+=+3sqrt%2810%29

Now you have: tan+%28A%29+=+y%2Fx+=+sqrt%2810%29%2F3sqrt%2810%29, or highlight_green%28tan+%28A%29+=+1%2F3%29



matrix%281%2C5%2Ctan+%28B%29%2Cis%2Cgiven%2Cas%2C4%2F3%29, so now you have all you need to find what you're looking for.