Show that cosθ. [(cosθ, sinθ)(-sinθ,cosθ)] + sinθ. [(sinθ,-cosθ)(cosθ, sinθ)] = 1

Question

Show that

\( cos\theta.\begin{bmatrix} cos\theta &sin\theta \\[0.3em] -sin\theta&cos\theta \\[0.3em] \end{bmatrix}+sin\theta.\) \( \begin{bmatrix} sin\theta & -cos\theta \\[0.3em] -sin\theta & sin\theta \\[0.3em] \end{bmatrix}=1\)

cosθ. [(cosθ, sinθ)(-sinθ,cosθ)] + sinθ. [(sinθ,-cosθ)(cosθ, sinθ)] = 1

Answer 1

We have to show that

Multiplying the scalars with we get,

And we know that cos²θ + sin²θ = 1

Hence, proved.