Question

Find theta such as tan(theta) = cot(theta+45). Thanks

Answer 1

cot(t+45) = cos(t+45)/sin(t+45)

so we have
sin t/cos t = [cos t cos 45 -sin t sin 45] / [sin t cos 45 + cos t sin 45]
but sin 45 = cos 45 = 1/sqrt 2
so
sin t[sin t/sqrt2+cost/sqrt2] = cost[cost/sqrt 2-sint/sqrt2]

sin^2t +sint cost = cos^2t -sint cost

sin^2 t + 2 sin t cos t - cos^2 t = 0

x^2+2xy-y^2 = 0
x = [-2y +/- sqrt(4y^2 +4y^2)]/2
x = -y +/- y sqrt 2
x = y ( -1+/- sqrt 2)
so
sin t = cos t (-1+/- sqrt 2)
tan t = .414 or -2.414
t = 22.5 or -67.5

check 22.5
.414 = .414 yes