Question 905071
{{{sin(A) = 1 - sqrt(2)}}}


{{{sin^2(A) = (1 - sqrt(2))^2}}}


{{{sin^2(A) = (1 - sqrt(2))(1 - sqrt(2))}}}


{{{sin^2(A) = 1(1 - sqrt(2))-sqrt(2)(1 - sqrt(2))}}}


{{{sin^2(A) = 1 - sqrt(2)-sqrt(2) +sqrt(2)*sqrt(2)}}}


{{{sin^2(A) = 1 - 2sqrt(2) +2}}}


{{{sin^2(A) = 3 - 2sqrt(2)}}}


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


{{{1 - sin^2(A) = cos^2(A)}}}


{{{1 - (3 - 2sqrt(2)) = cos^2(A)}}}


{{{1 - 3 + 2sqrt(2) = cos^2(A)}}}


{{{-2 + 2sqrt(2) = cos^2(A)}}}


{{{cos^2(A) = -2 + 2sqrt(2)}}}


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


{{{cos^2(A) + 2*sin(A)}}}


{{{-2 + 2sqrt(2) + 2*(1 - sqrt(2))}}}


{{{-2 + 2sqrt(2) + 2 - 2*sqrt(2)}}}


{{{0}}}


So this shows that {{{cos^2(A) + 2*sin(A) = 0}}} is true for every real number value of A. In other words, it is an identity.