(a) Tensile stress = normal force/area
and area = A/cosθ
Normal force = F cosθ
So, tensile stress = (F cosθ)/(A/cosθ) = F cos2θ/A
(b) Shearing stress = (Tangential force)/area
Tangential force = F sinθ
Area = A/cosθ
So, Shearing stress = (F sinθ)/(A/cosθ) = F/A sinθ cosθ
= F/2A x 2sinθcosθ = F/2A x sin 2θ
(c) Tensile stress will be maximum, when
cos2θ = maximum = 1
or, cosθ = 1 = cos 0° θ
or, θ = 0°
(d) Shearing stress will be maximum, when
sin 2θ = maximum = 1 = sin 90°
or, 2θ = 90°
or, θ = 45°