How do I solve for $\alpha$ and $\beta$ in terms of $\theta$ using the equations $$a^2 \cos^2\theta \:+\:b^2 \sin^2\theta \:=\:a^2\cos^2\alpha $$ and $$b^2 \cos^2\theta \:+\:a^2 \sin^2\theta \:=\:a^2\cos^2\alpha\ + a^2\sin^2\beta \sin^2\alpha$$
2026-05-16 12:00:07.1778932807
Solve for two variable in terms of other
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Hint: From the first equation you can immediately obtain $\alpha$. Then, in the second equation, plug in the first one and use that $\sin^2x+\cos^2x=1$.