How do I find individual values of $\sin(\varphi)$ and $\cos(\varphi)$ from $x = a\sin^{2}(\varphi) + b\cos^{2}(\varphi)$? If $x = a\sin^2\phi+ b\cos^2\phi$, express $\sin$ and $\cos$ in terms of $x$ ( $a$ and $b$ are real constants)
I know how to find values of $T$ ratios in equations like $x = a\sin^2t$ or $x = b\cos^2t$ but how do I find the values of $\sin(t)$ and $\cos(t)$
in expressions like $x = \sin^2t + 5\cos^2t$ or $x = a\sin t + b\cos t$?

1. $$x=a\sin^2\phi + b\cos^2\phi$$
2. $$x=a\sin^2\phi+b-b\sin^2\phi$$
3. $$x=b+(a-b)\sin^2\phi$$
4. $$\sin\phi=\pm\sqrt\frac{x-b}{a-b}$$
$$\cos\phi=\pm\sqrt\frac{a-x}{a-b}$$
Hope this helps!!
