Question 1153168
<br>
{{{(sin(41)+cos(41))^2 = 2sin^2(x)}}}<br>
Expand on the left:<br>
{{{sin^2(41)+2sin(41)cos(41)+cos^2(41) = 2sin^2(x)}}}<br>
Use sin^2+cos^2=1:<br>
{{{1+2sin(41)cos(41) = 2sin^2(x)}}}<br>
Use sin(2x) = 2sin(x)cos(x):<br>
{{{1+sin(82) = 2sin^2(x)}}}<br>
Solve for sin(x):<br>
{{{sin(x) = sqrt((1+sin(82))/2)}}}<br>
Use sin(x) = cos(90-x) for acute angles:<br>
{{{sin(x) = sqrt((1+cos(8))/2)}}}<br>
Use half angle formula for cosine:<br>
{{{sin(x) = cos(4)}}}<br>
Use sin(x) = cos(90-x) for acute angles:<br>
{{{sin(x) = sin(86)}}}<br>
ANSWER: 86 degrees<br>