# Obtaining theta for all trigonometric function sine and cos

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Obtaining theta for all trigonometric function sine and cos

obtaining all the result of trigonometric equation sine and cos of triangles ABC

Are there other ways of obtaining a result for the following trigonometric equations of $$\sin A$$ and $$\cos A$$ for all consecutive or non consecutive numbers $$x<y<z$$

$$(((\frac{\sqrt\frac{y}{z}}{(1-\frac{x}{z})\times\sqrt\frac{x+z}{z-x}})\times\frac{x}{z})+\sqrt\frac{z-y}{z})\times((1-\frac{x}{z})\times\sqrt\frac{(x+z)}{(z-x)})=\sin A$$

$$(\frac{\sqrt\frac{y}{z}}{(1-\frac{x}{z})\times\sqrt\frac{x+z}{z-x}})-(((\frac{\sqrt\frac{y}{z}}{(1-\frac{x}{z})\times\sqrt\frac{x+z}{z-x}})\times\frac{x}{z})+\sqrt\frac{z-y}{z})\times(\frac{x}{z})=\cos A$$

$$\sqrt\frac{(z-y)}{z}=\cos B$$

$$\sqrt\frac{y}{z}=\sin B$$

$$\frac{x}{z}=\cos C$$

$$((1-\frac{x}{z})\times\sqrt\frac{(z+x)}{(z-x)}=\sin C$$

The following variables a,b,c represent the length of the sides of the triangles.
$$\frac{\sin A}{\sin C}=a$$

$$\frac{\sin B}{\sin C}=b$$

$$\frac{\sin C}{\sin C}=c$$

$$\frac{h_c}{h_a}=a$$

$$\frac{h_c}{h_b}=b$$

$$\frac{h_c}{h_c}=c$$
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