Question

Please me with this!

Answer 1

`sin^(-1)(x) + cos^(-1)(-(1)/(2)) = \pi`

`sin[(sin^(-1)(x) + cos^(-1)(-(1)/(2))] = 0`

`sin(sin^(-1)(x)) \cdot cos(cos^(-1)(-(1)/(2))) + cos(sin^(-1)(x)) \cdot sin(cos^(-1)(-(1)/(2))) = 0`


`-(x)/(2) + \sqrt{1 - x^(2)} \cdot \sqrt{1 - (-(1)/(2))^(2)} = 0`

`\sqrt{1 - x^(2)} \cdot \sqrt{1 - ((1)/(4))} = (x)/(2)`

`\sqrt{1 - x^(2)} \cdot \sqrt{(3)/(4)} = (x)/(2)`


`\frac{\sqrt{3(1 - x^(2))}}{2} = (x)/(2)`

`\sqrt{3(1 - x^(2))} = x`

`3(1 - x^(2)) = x^(2)`

`3 - 3x^(2) = x^(2)`

`4x^(2) = 3`


`x^(2) = (3)/(4)`

`x = \pm (√(3))/(2)`

Substitute both x-values in, and only
`x = (√(3))/(2)` works.

Thus,
`x = (√(3))/(2)` is your solution.