PreCalc
posted by Joel .
If tan theta = 9/5 and cot omega = 9/5
Find the exact value of sin (omegatheta)

sorry that should be thetaomega not omegatheta

Cleverly, you note that since
tanθ = cotω, ω = π/2θ
Thus, θω = θ(π/2θ) = π/2+2θ
sin(θω) = cos2θ = 2sin^θ1
tanθ = 9/5, so
sinθ = 9/√106
sin(θω) = 162/106  1 = 56/106
or, if you must exercise your sum/difference formulas,
sin(θω) = sinθcosωcosθsinω
tanθ = 9/5, so
sinθ = 9/√106
cosθ = 5/√106
cotω = 9/5, so
sinω = 5/√106
cosω = 9/√106
sin(θω) = 9/√106 * 9/√106  5/√106 * 5/√106 = 56/106