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Question
Simplify, `cos theta[(cos theta, sintheta),(-sin theta, cos theta)] + sin theta [(sin theta, -cos theta), (cos theta, sin theta)]`
Solution
`cos theta[(cos theta ,sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, -cos theta),(cos theta, sin theta)]`
`= [(cos^2 theta, cos theta sin theta),(-sin thetacos theta, cos^2 theta)] + [(sin^2 theta, -sin thetacos theta),(sin thetacos theta, sin^2 theta)]`
`= [(cos^2 theta + sin^2 theta, cos theta sintheta-sin thetacos theta),(-sin thetacos theta+sin theta cos theta, cos^2 theta + sin^2 theta)]`
= `[(1,0),(0,1)]` ....(∵ `cos^2 theta + sin^2 theta = 1`)
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