Prove that `cos 4theta–cos 4alpha = 8(cos theta-cos alpha)(cos theta+ cos alpha )(cos theta -sin alpha)(cos theta+sin alpha)`

Prove that cos^(2)theta + cos^(2)(alpha + theta) – 2cos alpha *cos theta* cos(alpha +theta) is independent of theta .

if sin(theta+alpha)=cos(theta+alpha) then tan alpha

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

Show that cos^(2)theta+cos^(2)theta(alpha+theta)-2cos alpha cos theta cos(alpha+theta) is independent of theta.

If tan alpha=(sin theta-cos theta)/(sin theta+cos theta) then sin alpha

Show that: cos^(2)theta+cos^(2)(alpha+theta)-2cos alpha cos theta cos(alpha+theta) is independent of theta.

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)