SOLUTION: suppose A lies between 0 and 90 and {{{sec A + tan A = 4}}} determine cos(A)

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Question 1151777: suppose A lies between 0 and 90 and sec+A+%2B+tan+A+=+4 determine cos(A)
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
sec%28A%29+%2B+tan%28A%29+=+4

1%2Fcos%28A%29+%2B+sin%28A%29%2Fcos%28A%29+=+4

1%2Bsin%28A%29=4cos%28A%29

1%2Bsin%28A%29=4cos%28A%29

sin%28A%29=4cos%28A%29-1

sin%5E2%28A%29=%284cos%28A%29-1%29%5E2

sin%5E2%28A%29=16cos%5E2%28A%29-8cos%28A%29%2B1

1-cos%5E2%28A%29=16cos%5E2%28A%29-8cos%28A%29%2B1

8cos%28A%29=17cos%5E2%28A%29


8cos%28A%29-17cos%5E2%28A%29=0

cos%28A%29%288-17cos%28A%29%29=0

cos(A)=0;  8-17cos(A)=0
   A=90°;   -17cos(A)=-8
               cos%28A%29=%28-8%29%2F%28-17%29
               cos%28A%29=8%2F17

We discard 90° because neither sec(90°) nor tan(90°) 
which occur in the original equation are defined.

Answer: 8%2F17

Edwin