The question is:
tan(arcsinx)=
I know that inverse of sin is 1/sqrt(1-x^2) however this question still confuses me. The outcome is x/sqrt(1-x^2), how did the tan create the additional x ?
oops i think i meant to say that the derivative is 1/sqrt(1-x^2) dang I am tired.
so basically what i said in the original question is irrelevant.
To find the value of tan(arcsin(x)), we can use the relationship between the trigonometric functions sine (sin) and tangent (tan) and the definition of the inverse sine function (arcsin).
The relationship is as follows:
tan(arcsin(x)) = x / sqrt(1 - x^2)
Let's break down the steps to understand how we arrived at this result:
Step 1: Start with the equation tan(arcsin(x)).
Step 2: Substitute the value of arcsin(x) with a variable, let's say y. This gives us tan(y).
Step 3: Remember the definition of the inverse sine function: arcsin(x) = y means sin(y) = x. So we have sin(y) = x.
Step 4: Now, using the Pythagorean Identity sin^2(y) + cos^2(y) = 1, we can replace sin^2(y) with (1 - cos^2(y)).
Step 5: Rearranging the equation, we get cos^2(y) = 1 - x^2.
Step 6: Taking the square root of both sides, we have cos(y) = sqrt(1 - x^2).
Step 7: Since tan(y) = sin(y) / cos(y), we can substitute sin(y) with x and cos(y) with sqrt(1 - x^2) to get tan(arcsin(x)) = x / sqrt(1 - x^2).
The additional x in the result comes from substituting sin(y) = x into the expression for tan(y). The numerator x represents the sine function in this case.
So, tan(arcsin(x)) simplifies to x / sqrt(1 - x^2), which is the final answer.