SOLUTION: √3 tan A = 3 sinA to find value of cos square A -sin square A

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Question 1042102: √3 tan A = 3 sinA to find value of cos square A -sin square A
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
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sqrt(3)*tan(A) = 3*sin(A). Find value of cos%5E2%28A%29+-sin%5E2%28A%29.
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Notice that I edited your post . . . 

sqrt%283%29%2Atan%28A%29 = 3%2Asin%28A%29  --->  sqrt%283%29%2A%28sin%28A%29%2Fcos%28A%29%29 = 3%2Asin%28A%29  --->  1%2Fcos%28A%29 = 3%2Fsqrt%283%29  --->  cos(A) = sqrt%283%29%2F3%29.

If  cos(A) = sqrt%283%29%2F3%29  then  sin(A) = sqrt%281-cos%5E2%28A%29%29 = sqrt%281-%28sqrt%283%29%2F3%29%5E2%29 = sqrt%281-3%2F9%29 = sqrt%286%2F9%29 = +/-sqrt%286%29%2F3.

Now,  cos%5E2%28A%29+-sin%5E2%28A%29 = %28sqrt%283%29%2F3%29%5E2 - %28sqrt%286%29%2F3%29%5E2 = 3%2F9+-+6%2F9 = -3%2F9 = -1%2F3.

Answer.  cos%5E2%28A%29+-sin%5E2%28A%29 =  -1%2F3.