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

解

解く

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

すべての t で真; arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))

解答ステップ

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

簡素化

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 ) )})

括弧を削除する:

(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}))

両側は等しい

すべての t で真; arccos (\frac{5 cos ( x ) + 3}{5 + 3 cos ( x )}) = 2 arctan (\frac{1}{2} tan (\frac{x}{2}))