if `cos theta - sin theta = sqrt(2)sintheta`, show that `costheta + sin theta = sqrt(2) costheta`

If costheta+sintheta=sqrt2costheta ,then show that costheta-sintheta=sqrt2 sintheta .

If sin theta-sqrt(6)costheta=sqrt(7)costheta. Prove that cos theta-sqrt6 sin theta-sqrt7 sin theta=0.

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 / 7) is

Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4) .

Simplify, costheta[[cos theta, sin theta],[-sin theta, cos theta]] + sin theta [[sin theta, -cos theta],[cos theta, sin theta]]

If acos theta-b sin theta=c , show that asin theta+b cos theta=+-sqrt(a^2+b^2-c^2dot)

Prove that : sin 2 theta= 2sin theta cos theta .

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .