1.

Write the following functions in the simplest form : tan^(-1) (x/sqrt(a^2-x^2)), |x| lt a

Answer»

Solution :PUT x = a `SIN theta, theta = sin^(-1)(x/a)`
Then `TAN^(-1)(x/sqrt(a^2-x^2)) = tan^(-1)((a sin theta)/sqrt(a^2-a^2 sin^2 theta ))`
`= tan^(-1)((a sin theta)/sqrt(a^2 cos^2 theta)) = tan^(-1) (tan theta) = theta = sin^(-1)(x/a)`


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