SOLUTION: given that sin A = 1 - sqrt(2) show that cos^2A +2SinA = 0

Algebra ->  Trigonometry-basics -> SOLUTION: given that sin A = 1 - sqrt(2) show that cos^2A +2SinA = 0      Log On


   

Question 905071: given that sin A = 1 - sqrt(2) show that cos^2A +2SinA = 0
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28A%29+=+1+-+sqrt%282%29

sin%5E2%28A%29+=+%281+-+sqrt%282%29%29%5E2

sin%5E2%28A%29+=+%281+-+sqrt%282%29%29%281+-+sqrt%282%29%29

sin%5E2%28A%29+=+1%281+-+sqrt%282%29%29-sqrt%282%29%281+-+sqrt%282%29%29

sin%5E2%28A%29+=+1+-+sqrt%282%29-sqrt%282%29+%2Bsqrt%282%29%2Asqrt%282%29

sin%5E2%28A%29+=+1+-+2sqrt%282%29+%2B2

sin%5E2%28A%29+=+3+-+2sqrt%282%29

-------------------------------------------------------

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

1+-+%283+-+2sqrt%282%29%29+=+cos%5E2%28A%29

1+-+3+%2B+2sqrt%282%29+=+cos%5E2%28A%29

-2+%2B+2sqrt%282%29+=+cos%5E2%28A%29

cos%5E2%28A%29+=+-2+%2B+2sqrt%282%29

--------------------------------------------------------

cos%5E2%28A%29+%2B+2%2Asin%28A%29

-2+%2B+2sqrt%282%29+%2B+2%2A%281+-+sqrt%282%29%29

-2+%2B+2sqrt%282%29+%2B+2+-+2%2Asqrt%282%29

0

So this shows that cos%5E2%28A%29+%2B+2%2Asin%28A%29+=+0 is true for every real number value of A. In other words, it is an identity.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
given that sin A = 1 - sqrt(2) show that cos^2A +2SinA = 0
***
sinA=1-sqrt%282%29
cos%5E2%28A%29%2B2sin%28A%29
1-sin%5E2%28A%29%2B2%281-sqrt%282%29%29
1-%281-2sqrt%282%29%2B2%29%2B2-2sqrt%282%29
1-1%2B2sqrt%282%29-2%2B2-2sqrt%282%29=0