Simplify the expression. tan(sin^-1(x)) i need steps for this problem

### 4 Answers

tan [sin^-1 (x)] let u = sin^-1 (x) so, sin u = x now u draw a right-angled triangle with an angle u : from sin u = x , the opp. is x and the hypotenus is 1, then u find the adj. which is √(1 – x^2) tan [sin^-1 (x)] = tan u = opp./adj. = x / √(1 – x^2) therefore tan [sin^-1 (x)] = x / √(1 – x^2)

Simplify This Expression

If by sin^-1(x) you mean the inverse function of sin then proceed otherwise disregard this this answer. OK so think that sin^-1(x) = T then by applying the sin function to both sides we have sin(sin^-1(x)) = sin(T) x = sin(T) so, sin(T) = x now since sin(T) = opposite/hypotenuse = x so let the hypotenuse = 1 so the opposite side of T = x so we need to find the measurement of the side adjacent to T using the Pythagorean theorem we get the square root of (1 – x^2) now since tan = opposite/adjacent we have tan(sin^-1(x)) = tan(T) = x / [root(1-x^2) ]

draw a right angled triangle, with hypotenuse = 1, side=x —>other side = sqrt(1-x^2)

Hence tan(sin^-1(x)) = x/sqrt(1-x^2)