 In this video we present the solution to question number eight for exam practice exam number one for math 12 10 In which case we're asked to write tangent of cosine of inverse of x as an equivalent expression involving only the x That is we want to rewrite it algebraically And so my recommendation is to use a triangle diagram to help you Handle these type of problems right here, which we're going to be considering the angle theta But what is theta right here? Well the inverse trigonometric function is the theta value So we have that theta is equal to cosine inverse of x Well since theta is equal to cosine inverse of x that means cosine of theta is equal to x But we want to think this is a ratio x over 1 So using our so katoha since cosine is adjacent over hypotenuse We're going to label the adjacent side as x the hypotenuse as 1 and then using the Pythagorean equation We know that the adjacent side squared plus the opposite side squared is going to equal the hypotenuse squared And so solving for the opposite side right here We're going to see that the opposite side is the square root of 1 minus x squared So now we have to compute tangent of theta That's what our goal is tangent of theta. Well tangent of theta is going to be opposite over adjacent And so we're going to take the opposite side, which is the square root of 1 minus x squared over the adjacent side Which is x and so then we see the correct answer will be option D