SOLUTION: If 0 < A < pi/2 and sinA + 1 = 2 sqrt(1-sin^2 A), determine the value of sinA.

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Question 1176721: If 0 < A < pi/2 and sinA + 1 = 2 sqrt(1-sin^2 A), determine the value of sinA.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If 0+%3C+A+%3C+pi%2F2+and sin%28A%29+%2B+1+=+2+sqrt%281-sin%5E2%28+A%29%29, determine the value of sin%28A%29.
sin%28A%29+%2B+1+=+2sqrt%281-sin%5E2%28A%29%29.......square both sides
%28sin%28A%29+%2B+1%29%5E2+=+%282sqrt%281-sin%5E2%28A%29%29%29%5E2
%28sin%28A%29+%2B+1%29%5E2+=+4%281-sin%5E2%28A%29%29
sin%5E2%28A%29+%2B2sin%28A%29%2B+1=+4-4sin%5E2%28A%29
sin%5E2%28A%29+%2B4sin%5E2%28A%29%2B2sin%28A%29%2B+1-+4=0
5sin%5E2%28A%29%2B2sin%28A%29-+3=0......factor
5sin%5E2%28A%29-3sin%28A%29%2B5sin%28A%29-+3=0
%285sin%5E2%28A%29-3sin%28A%29%29%2B%285sin%28A%29-+3%29=0
sin%28A%29%285sin%5E2%28A%29-3%29%2B%285sin%28A%29-+3%29=0
%28sin%28A%29+%2B+1%29+%285sin%28A%29+-+3%29+=+0
solutions:
if sin%28A%29+%2B+1+=+0+=> sin%28A%29+=-1+
if 5sin%28A%29+-+3+=+0=> sin%28A%29+=3%2F5


A=sin%5E-1%28-1%29+=-pi%2F2 ...........since given 0+%3C+A+%3C+pi%2F2, that is not solution
so, the value of sin%28A%29 is 3%2F5=> your solution
if you want angle in degrees, it is
A=sin%5E-1%283%2F5%29+=36.87°