Evaluate: `|[cos theta, 0, sin theta], [ 0,1,0], [-sin theta , 0, costheta]|`

Evaluate the following: |costheta, -sin theta],[sin theta, cos theta]|

sin theta -cos theta=0

If cos2theta=0 , then |(0,costheta,sin theta),(cos theta, sin theta, 0),(sin theta, 0, cos theta)|^(2) is equal to…………

2sin^(2)theta + 3 costheta =0

Evaluate [[sin^2 theta, 1],[cos^2 theta, 0]]+[[cos^2 theta, 0],[-cosec^2 theta, 1]]+[[0,-1],[-1,0]]

If f(x)=|{:( sin^2 theta , cos^(2) theta , x),(cos^(2) theta , x , sin^(2) theta ),( x , sin^(2) theta , cos^2 theta ):}| theta in (0,pi//2), then roots of f(x)=0 are

Solve 2 cos^(2) theta +3 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

Solve sin2theta+costheta=0

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1