solvefor x,arcsin(x)+arcsin(y)= pi/2

解答

求解

x, arcsin (x) + arcsin (y) = \frac{π}{2}

x = sin (\frac{π}{2} - arcsin (y))

求解步骤

arcsin (x) + arcsin (y) = \frac{π}{2}

将

arcsin (y)

到右边

arcsin (x) + arcsin (y) = \frac{π}{2}

两边减去

arcsin (y)

arcsin (x) + arcsin (y) - arcsin (y) = \frac{π}{2} - arcsin (y)

化简

arcsin (x) = \frac{π}{2} - arcsin (y)

arcsin (x) = \frac{π}{2} - arcsin (y)

使用反三角函数性质

arcsin (x) = \frac{π}{2} - arcsin (y)

arcsin (x) = a \Rightarrow x = sin (a)

x = sin (\frac{π}{2} - arcsin (y))

x = sin (\frac{π}{2} - arcsin (y))

2 arctan (\frac{1}{2}) = arccos (x)

sin (\frac{x}{2}) + sin (\frac{x}{2}) = sin (x)

15 cos (x) - 5 = 4 cos (x)

cos (x) - cos (2 x) = 0, 0 \leq x \leq 2 π

2 + cos (2 x) = - 5 sin (x)