Question

The sum of the three smallest positive values of theta such that `4(costheta)(sintheta) = 1" is "k*pi.` Find k?

Answer 1

`4costhetasintheta = 1`

`=>2costhetasintheta = 1/2`

`=>sin2theta = sin(pi/6)`

`=>2theta=npi+(-1)^n*(pi/6)`

`=>theta=1/2(npi+(-1)^n*(pi/6)) "where "ninZZ`

When `n=0totheta=pi/12`

When `n=1totheta=(5pi)/12`

When `n=2totheta=(13pi)/12`

By the condition of the problem

`pi/12+(5pi)/12+(13pi)/12=kpi`

So `k=19/12`