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