Question 1153087
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{{{sin(A)+1=2*sqrt(1-sin^2(A))}}}<br>
Square both sides:<br>
{{{sin^2(A)+2*sin(A)+1 = 4(1-sin^2(A)) = 4-4sin^2(A)}}}<br>
{{{5sin^2(A)+2sin(A)-3 = 0}}}<br>
Solve the quadratic equation by factoring:<br>
{{{(5sin(A)-3)(sin(A)+1) = 0}}}<br>
{{{sin(A) = 3/5}}} OR {{{sin(A) = -1}}}<br>
The restriction {{{0<A<pi/2}}} means sin(A) has to be between 0 and 1, so....<br>
ANSWER: sin(A) = 3/5<br>