Remove parentheses.
\[provethat(\cos{e})c\times \frac{x}{4}+(\cos{e})c\times \frac{x}{2}+(\cos{e})cx=\cot{\frac{x}{8}}-\cot{x}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{provethat(\cos{e})cx}{4}+(\cos{e})c\times \frac{x}{2}+(\cos{e})cx=\cot{\frac{x}{8}}-\cot{x}\]
Use Product Rule : \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{prove{t}^{2}ha(\cos{e})cx}{4}+(\cos{e})c\times \frac{x}{2}+(\cos{e})cx=\cot{\frac{x}{8}}-\cot{x}\]
Regroup terms.
\[\frac{e(\cos{e})prov{t}^{2}hacx}{4}+(\cos{e})c\times \frac{x}{2}+(\cos{e})cx=\cot{\frac{x}{8}}-\cot{x}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{e(\cos{e})prov{t}^{2}hacx}{4}+\frac{(\cos{e})cx}{2}+(\cos{e})cx=\cot{\frac{x}{8}}-\cot{x}\]
Simplify \(\frac{e(\cos{e})prov{t}^{2}hacx}{4}+\frac{(\cos{e})cx}{2}+(\cos{e})cx\) to \(\frac{e(\cos{e})prov{t}^{2}hacx}{4}+\frac{3(\cos{e})cx}{2}\).
\[\frac{e(\cos{e})prov{t}^{2}hacx}{4}+\frac{3(\cos{e})cx}{2}=\cot{\frac{x}{8}}-\cot{x}\]
Factor out the common term \((\cos{e})cx\).
\[(\cos{e})cx(\frac{eprov{t}^{2}ha}{4}+\frac{3}{2})=\cot{\frac{x}{8}}-\cot{x}\]
Divide both sides by \(\cos{e}\).
\[cx(\frac{eprov{t}^{2}ha}{4}+\frac{3}{2})=\frac{\cot{\frac{x}{8}}-\cot{x}}{\cos{e}}\]
Divide both sides by \(c\).
\[x(\frac{eprov{t}^{2}ha}{4}+\frac{3}{2})=\frac{\frac{\cot{\frac{x}{8}}-\cot{x}}{\cos{e}}}{c}\]
Simplify \(\frac{\frac{\cot{\frac{x}{8}}-\cot{x}}{\cos{e}}}{c}\) to \(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})c}\).
\[x(\frac{eprov{t}^{2}ha}{4}+\frac{3}{2})=\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})c}\]
Divide both sides by \(x\).
\[\frac{eprov{t}^{2}ha}{4}+\frac{3}{2}=\frac{\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})c}}{x}\]
Simplify \(\frac{\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})c}}{x}\) to \(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}\).
\[\frac{eprov{t}^{2}ha}{4}+\frac{3}{2}=\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}\]
Subtract \(\frac{3}{2}\) from both sides.
\[\frac{eprov{t}^{2}ha}{4}=\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2}\]
Multiply both sides by \(4\).
\[eprov{t}^{2}ha=(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})\times 4\]
Regroup terms.
\[eprov{t}^{2}ha=4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})\]
Divide both sides by \(e\).
\[prov{t}^{2}ha=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{e}\]
Divide both sides by \(r\).
\[pov{t}^{2}ha=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{e}}{r}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{e}}{r}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{er}\).
\[pov{t}^{2}ha=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{er}\]
Divide both sides by \(o\).
\[pv{t}^{2}ha=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{er}}{o}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{er}}{o}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{ero}\).
\[pv{t}^{2}ha=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{ero}\]
Divide both sides by \(v\).
\[p{t}^{2}ha=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{ero}}{v}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{ero}}{v}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov}\).
\[p{t}^{2}ha=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov}\]
Divide both sides by \({t}^{2}\).
\[pha=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov}}{{t}^{2}}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov}}{{t}^{2}}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}}\).
\[pha=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}}\]
Divide both sides by \(h\).
\[pa=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}}}{h}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}}}{h}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}h}\).
\[pa=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}h}\]
Divide both sides by \(a\).
\[p=\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}h}}{a}\]
Simplify \(\frac{\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}h}}{a}\) to \(\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}ha}\).
\[p=\frac{4(\frac{\cot{\frac{x}{8}}-\cot{x}}{(\cos{e})cx}-\frac{3}{2})}{erov{t}^{2}ha}\]
p=(4*((cot(x/8)-cot(x))/(cos(e)*c*x)-3/2))/(e*r*o*v*t^2*h*a)
