Find `|[sin theta, costheta], [-sin theta, costheta]|`

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

The value of the determinant |(sintheta, costheta, sin2theta) , (sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)) , (sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3))|

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

The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

if A=[{:(costheta,sin theta ),(-sin theta,costheta):}] , then show that : A^(2)=[{:(cos2theta,sin2theta),(-sin2theta,cos2theta):}]

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

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

If 5 tan theta = 4 , find the value of : (8 sin theta-3costheta)/(8 sin theta+2costheta)

costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]=?

Solve sin2theta+costheta=0