Which one is greater: `cos(log_e theta)or log_e(costheta)` if `-pi/2ltthetaltpi/2`

The larger of cos(log theta) and log(cos theta) if (pi)/(2)

The larger of cos(ln theta) and ln(cos theta) if e^(-(pi)/(2))

int cos (log_e x)dx is equal to

The number of solutions of the equation (log_(2)cos theta)^(2)+log.(4)/(cos theta) (16 cos theta)=2 in the interval [0, 2pi) is

Which is smaller 2or (log_(pi)2+log_(2)pi)

The correct curve between log_(e) R and log_(e) (theta - theta_(o) ) is -

Prove that int_(0)^(2pi)e^(costheta)cos(sintheta)d theta=2pi .