SOLUTION: if tanA+secA= 3 then find tha value of sinA.

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Question 394612: if tanA+secA= 3 then find tha value of sinA.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite everything in terms of sin(A) and cos(A) to get

sin%28A%29%2Fcos%28A%29+%2B+1%2Fcos%28A%29+=+3

%28sin%28A%29+%2B+1%29%2Fcos%28A%29+=+3

sin%28A%29+%2B+1+=+3+cos+%28A%29 I'll rewrite cos%28A%29 as sqrt%281-sin%5E2%28A%29%29

sin%28A%29+%2B+1+=+3sqrt%281+-+sin%5E2+%28A%29%29

Squaring both sides,

sin%5E2+%28A%29+%2B+2sin%28A%29+%2B+1+=+9+-+9+sin%5E2+%28A%29 Let u+=+sin%5E2+%28A%29. It is easy to see that we can now obtain a quadratic:

10u%5E2+%2B+2u+-+8+=+0 --> 5u%5E2+%2B+u+-+4+=+0

u+=+%28-1+%2B-+sqrt%281+%2B+80%29%29%2F10+=+%28-1+%2B-+9%29%2F10 = -1 or 4/5. These values are between -1 and 1 inclusive, so these are the two possible values for sin(A).