`(sin 2 theta cos theta- cos 2 theta sin theta)/(cos 2 theta cos theta+ sin 2 theta sin theta) = tan theta`

cos theta+sin theta=cos2 theta+sin2 theta

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

If f(theta)=|(cos^(2) theta, cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2) theta, cos theta),(sin theta, -cos theta, 0)| then f((pi)/12)=

(cos theta-sin theta) / (cos theta + sin theta) = sec2 theta-tan2 theta

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta

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

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

(sin theta+sin2 theta)/(1+cos theta+cos2 theta)=tan theta=sin theta*sec theta

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta