Question

Question #3a4af

Answer 1

`"the Soln. Set="{2kpi+-pi}uu{2kpi+-pi/3}, k in ZZ.`

Explanation:

Given that, `sin(x/2)=cosx,` and we seek for the soln. of this

trgo. eqn.

We replace `sin(x/2)" by "sqrt((1-cosx)/2),` & get,

`sqrt((1-cosx)/2)=cosx.`

`:. (1-cosx)/2=cos^2x.`

`:. 2cos^2x+cosx-1=0.`

`:. (cosx+1)(2cosx-1)=0.`

`:, cosx=-1=cospi, or, cosx=1/2=cos(pi/3).`

Knowing hat, `costheta=cosalpha rArr theta=2kpi+-alpha, k in ZZ,` we have,

`theta=2kpi+-pi, or, theta=2kpi+-pi/3, k in ZZ.`

Hence, `"the Soln. Set="{2kpi+-pi}uu{2kpi+-pi/3}, k in ZZ.`