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Question
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = pi/2, x != 0`
Solution
`sin^(-1) (5/x) + sin^(-1) (12/x) = pi/2`
`sin^(-1) + cos^(-1) sqrt(1-144/x^2) = pi/2`
Let `sin^(-1) 12/x = beta`
`12/x = sin beta = "OPP"/"HYP"`
`sqrt(x^2 - 144)/x = cos beta = "adj"/"HYP"`
`beta = cos^(-1) (sqrt(x^2 - 144)/x^2)`
`:. 5/x = sqrt(1- 144/x^2)`
`25/x^2 = 1 - 144/x^2`
`169/x^2 = 1`
`x^2 = 169`
x = 13
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