Question 15
Given that
$$\frac{\cos^4\alpha}{\cos^2\beta}+\frac{\sin^4\alpha}{\sin^2\beta}=1,$$
evaluate the expression printed in the source as
$$\frac{\cos^4\beta}{\cos^2\alpha}+\frac{\sin^4\alpha\beta}{\sin^2\alpha},$$
using the explicit notation correction stated below.
Notation correction for answering: the original second target numerator is printed as $\sin^4\alpha\beta$, an ambiguous extra-symbol expression. Read it here as $\sin^4\beta$, so the target is $\dfrac{\cos^4\beta}{\cos^2\alpha}+\dfrac{\sin^4\beta}{\sin^2\alpha}$. This is an explicit editorial interpretation, not an exact transcription of that numerator. All options remain as printed, and all denominators must be nonzero.
Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.
$$\frac{\cos^4\alpha}{\cos^2\beta}+\frac{\sin^4\alpha}{\sin^2\beta}=1,$$
evaluate the expression printed in the source as
$$\frac{\cos^4\beta}{\cos^2\alpha}+\frac{\sin^4\alpha\beta}{\sin^2\alpha},$$
using the explicit notation correction stated below.
Notation correction for answering: the original second target numerator is printed as $\sin^4\alpha\beta$, an ambiguous extra-symbol expression. Read it here as $\sin^4\beta$, so the target is $\dfrac{\cos^4\beta}{\cos^2\alpha}+\dfrac{\sin^4\beta}{\sin^2\alpha}$. This is an explicit editorial interpretation, not an exact transcription of that numerator. All options remain as printed, and all denominators must be nonzero.
Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.