Resol sina=sqrt{b}(1-sin^2a)

$$\sin a = \sqrt { b } ( 1 - \sin ^ { 2 } a )$$

Resoleu b

$$b=\frac{\left(\tan(a)\right)^{2}}{\left(\cos(a)\right)^{2}}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\left(a\geq 2\pi n_{1}\text{ and }a<2\pi n_{1}+\frac{\pi }{2}\right)\text{ or }\left(a>2\pi n_{1}+\frac{\pi }{2}\text{ and }a\leq 2\pi n_{1}+\pi \right)\right)$$

Passos per resoldre equacions radicals

Intercanvieu els costats perquè tots els termes variables estiguin al costat esquerre.

$$\sqrt{b}\left(1-\left(\sin(a)\right)^{2}\right)=\sin(a)$$

Utilitzeu la propietat distributiva per multiplicar \sqrt{b} per 1-\left(\sin(a)\right)^{2}.

$$\sqrt{b}-\sqrt{b}\left(\sin(a)\right)^{2}=\sin(a)$$

Combineu tots els termes que continguin b.

$$\left(1-\left(\sin(a)\right)^{2}\right)\sqrt{b}=\sin(a)$$

Dividiu els dos costats per 1-\left(\sin(a)\right)^{2}.

$$\frac{\left(-\left(\sin(a)\right)^{2}+1\right)\sqrt{b}}{-\left(\sin(a)\right)^{2}+1}=\frac{\sin(a)}{-\left(\sin(a)\right)^{2}+1}$$

En dividir per 1-\left(\sin(a)\right)^{2} es desfà la multiplicació per 1-\left(\sin(a)\right)^{2}.

$$\sqrt{b}=\frac{\sin(a)}{-\left(\sin(a)\right)^{2}+1}$$

Dividiu \sin(a) per 1-\left(\sin(a)\right)^{2}.

$$\sqrt{b}=\frac{\tan(a)}{\cos(a)}$$

Eleveu els dos costats de l'equació al quadrat.

$$b=\frac{\left(\tan(a)\right)^{2}}{\left(\cos(a)\right)^{2}}$$

Resoleu b (complex solution)

$$b=\frac{4\left(\sin(a)\right)^{2}}{\left(\cos(2a)+1\right)^{2}}$$

$$\left(\nexists n_{3}\in \mathrm{Z}\text{ : }a=\frac{\pi n_{3}}{2}\text{ and }arg(\frac{\sin(a)}{\cos(2a)+1})<\pi \right)\text{ or }\left(\exists n_{2}\in \mathrm{Z}\text{ : }a=\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }a=\frac{\pi \left(2n_{1}+1\right)}{2}\right)$$