IF theta-phi=pi/2 , then show that [{:(c...

IF `theta-phi=pi/2` , then show that `[{:(cos^2theta,costhetasintheta),(costhetasintheta,sin^2theta):}][{:(cos^2phi,cosphisinphi),(cosphisinphi,sin^2phi):}]=O`

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If 2-cos^(2)theta = 3 sin theta cos theta then theta =

`n pi + (pi)/(3) : n in Z`

`n pi + Tan^(-1)(1//2) : n in Z` or `n pi + (pi)/(4) : n in Z`

`n pi + (-1)^(n)(pi)/(6) : n in Z`

`n pi - Tan^(-1)(3//2) : n in Z` or `n pi + Tan^(-1) (1//4) : n in Z`

(cos theta + sin theta )^(2) + (cos theta - sin theta )^(2) =

`sqrt(2)`

If sin(pi cos theta)=cos(pi sin theta) then sin2theta=

`+-3/4`

`+-1/3`

`+-2/3`

`+-1/4`