Statics question about friction on inclined

Question

A body of weight (W) is placed on a rough inclined plane makes with the horizontal an angle of measure θ and the force of magnitude (W) acts on it in direction of the line of greatest slope of the plane and the body is about to move up , then μs + tanθ= .........

a) secθ

b) cscθ

c) sinθ

d) cosθ

## I need the solution with detailed steps (why) ##

Answer 1

Her mg = W and F = W

Asd the body is about to move up

Force of friction ACTS downwards along the p[lane

Normal reaction = W cos theta

Force of friction = µs W cos theta

Force along the plane downwards = W Sin theta

So eqation of motion is

µs W cos theta + W sin theta = W.... Equation 1

Dividing by Wcos theta

µs + tan theta = 1/ cos theta = Sec theta

So answer a is correct choice

So answer A is correct