Simplify tan(arccos(6x))

Problem

tan(arccos(6*x))

Solution

1. Identify the inner function as an angle θ=arccos(6*x) which implies cos(θ)=6*x

2. Represent the relationship using a right triangle where the adjacent side is 6*x and the hypotenuse is 1

3. Determine the opposite side of the triangle using the Pythagorean theorem: a2+b2=c2

4. Solve for the opposite side: opposite=√(,1−(6*x)2)=√(,1−36*x2)

5. Apply the definition of the tangent function, which is the ratio of the opposite side to the adjacent side: tan(θ)=opposite/adjacent

6. Substitute the expressions for the sides to find the final simplified form: √(,1−36*x2)/(6*x)

Final Answer

tan(arccos(6*x))=√(,1−36*x2)/(6*x)

Want more problems? Check here!