Consider the figure given below in which a particle of weight W resting a smooth (frictional less) inclined plain AB with the help of force F acting on the particle at angle θ with the line AB.

find the force F and normal reaction.

(Wsinα)/cosθ, [Wcos(α + θ)]/cosθ

By : Law of Sine

F/sin(180 - α) = N/sin(90 + α + θ) = W/sin(90 - θ)

On solving this, we get : $F = (W \sinα)/\cosθ, N = [W \cos(α + θ)]/ \cosθ$