If alpha=sin^(-1)(2/3)" and "beta=tan^(-...

If `alpha=sin^(-1)(2/3)" and "beta=tan^(-1)(1/2)`, where `0lt alpha,betalt(pi)/(2),` then find the value of `alpha-beta`.

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The correct Answer is:

`tan^(-1)[(5sqrt(5)-9)/(8)]`

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