sin^2(3 theta+5pie)+cos^2(3 theta+5pie)= ?

To simplify the expression sin^2(3θ+5π) + cos^2(3θ+5π), we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.

In this case, we have sin^2(3θ+5π) + cos^2(3θ+5π). Since the angles inside the sin^2 and cos^2 are the same, we can apply the identity:

sin^2(3θ+5π) + cos^2(3θ+5π) = 1.

Therefore, the expression sin^2(3θ+5π) + cos^2(3θ+5π) equals 1.