Consider the cubic equation `x^3-(1+cos theta+sin theta)x^2+(cos theta sin theta+cos theta+sin theta)x-sin theta. cos theta =0` Whose roots are `x_1, x_2 and x_3`

cosider the cubic equation : x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta+cos theta+sin theta)x-sin theta cos theta=0 whose roots are x_(1),x_(2),x_(3) .The value of (x_(1))^(2)+(x_(2))^(2)+(x_(3))^(2) equals

(cos theta)/(1-sin theta)=(1+cos theta+sin theta)/(1+cos theta-sin theta)

8sin theta cos theta cos2 theta cos4 theta=sin x the x=

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

(1+cos theta+sin theta)/(1+cos theta-sin theta)=(1+sin theta)/(cos theta)

sin theta+sin2 theta+sin3 theta=1+cos theta+cos2 theta

Prove (cos theta)/(1-sin theta)=(1+cos theta+sin theta)/(1+cos theta-sin theta)

(1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

8sin theta cos theta cos2 theta cos4 theta=sin x rArr x=

(sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)