solvefor t,arccos(((5cos(x)+3))/((5+3cos(x))))=2arctan(1/2*tan(x/2))

Lösung

löse nach

t, arccos (\frac{( 5 cos ( x ) + 3 )}{( 5 + 3 cos ( x ) )}) = 2 arctan (\frac{1}{2} \cdot tan (\frac{x}{2}))

Wahr f \overset{u}{¨} r alle t; arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))

Schritte zur Lösung

arccos (\frac{( 5 cos ( x ) + 3 )}{( 5 + 3 cos ( x ) )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))

Vereinfache

arccos (\frac{( 5 cos ( x ) + 3 )}{( 5 + 3 cos ( x ) )}) : arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )})

arccos (\frac{( 5 cos ( x ) + 3 )}{( 5 + 3 cos ( x ) )})

Entferne die Klammern:

(a) = a

= arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )})

arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))

Beide Seiten sind gleich

Wahr f \overset{u}{¨} r alle t; arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))

so l v e f or x, y = cos (\frac{y}{1.75}) + x - 0.5 y^{2}

so l v e f or c, 2 sin^{3} (x) + cos^{2} (x) - cos (x) = 0

so l v e f or i, sin (x^{2}) + cos^{2} (x) + sin (x) + 1 = 0

so l v e f or t, tan^{2} (x) cot (x) = 1 + sec^{2} (x)

so l v e f or i, cos^{3} (x) + 2 sin (x) - 5 sin^{3} (x) = 0