Question

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

Answer 1

We have
`costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]`
`=[{:(cos^(2)theta,sinthetacostheta),(-sinthetacostheta,cos2theta):}]+[{:(" "sin^(2)theta,-sinthetacostheta),(sinthetacostheta," "sin^(2)theta):}]`
`[{:(" "cos^(2)theta+sin^(2)theta,sinthetacostheta+(-sinthetacostheta)),(-sinthetacostheta+sinthetacostheta," "cos^(2)theta+sin^(2)):}]`
`=[{:(1,0),(0,1):}].`