The passive earth pressure of a soil, is proportional to (where φ is the angle of internal friction of the soil.)

ANS:D - tan² (45° + φ)

For active case;
Ka =tan^2(45-π/2)

And for the passive case,
it is Kp=tan^2(45+π/2). Earth pressure at rest proportional to =(1-sinθ).
Active earth pressure proportional to = cotθ (45°+ φ/2) or tanθ (45°- φ/2).
Passive earth pressure proportional to = tanθ (45°+ φ/2). The Right answer is tan^2(45π/2).
For Active earth pressure: tan^2(45+π/2).
Earth pressure at rest :( 1-sinθ).