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

Postby Guest » Mon Feb 26, 2018 6:54 pm

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 [tex]\sin A[/tex] and [tex]\cos A[/tex] for all consecutive or non consecutive numbers [tex]x<y<z[/tex]


[tex](((\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[/tex]

[tex](\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[/tex]

[tex]\sqrt\frac{(z-y)}{z}=\cos B[/tex]

[tex]\sqrt\frac{y}{z}=\sin B[/tex]

[tex]\frac{x}{z}=\cos C[/tex]

[tex]((1-\frac{x}{z})\times\sqrt\frac{(z+x)}{(z-x)}=\sin C[/tex]

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

[tex]\frac{\sin B}{\sin C}=b[/tex]

[tex]\frac{\sin C}{\sin C}=c[/tex]

[tex]\frac{h_c}{h_a}=a[/tex]

[tex]\frac{h_c}{h_b}=b[/tex]

[tex]\frac{h_c}{h_c}=c[/tex]

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