Answer:
see below
Explanation:
sin x = cos x
opp/ hyp = adj /hyp
Multiply each side by the hypotenuse
opp = adj
The opposite side must equal the adjacent
Since this is a right triangle
opp ^2 + adj ^2 = hypotenuse^2
opp ^2 + opp ^2 = hypotenuse^2
2 opp ^2 = hypotenuse^2
Take the square root of each side
sqrt(2 opp ^2) =sqrt( hypotenuse^2)
sqrt(2) opp = hyp
We know sin X = opp / hyp
sin x = opp / (sqrt(2) / hyp)
sin x = 1 / sqrt(2)
sin x = sqrt(2) /2
Taking the inverse sin of each side
x = sin ^-1 ( sqrt(2) /2)