If p₁ and p₂ are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle $${\theta ^ \circ }$$ to the principal plane carrying the principal stress p₁, is:

A. $$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\sin \,2\theta $$

B. $$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\cos\,2\theta $$

C. $$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\cos\,2\theta $$

D. $$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\sin \,2\theta $$

Answer: Option C