Simplify tan(arccos(7x))

Problem

tan(arccos(7*x))

Solution

1. Identify the inner function as an angle θ=arccos(7*x) which implies cos(θ)=7*x

2. Visualize a right triangle where the adjacent side is 7*x and the hypotenuse is 1

3. Apply the Pythagorean theorem to find the length of the opposite side, a2+b2=c2

4. Solve for the opposite side: opposite=√(,1−(7*x)2)=√(,1−49*x2)

5. Use the definition of the tangent function, which is the ratio of the opposite side to the adjacent side.

6. Substitute the side lengths into the ratio: tan(θ)=√(,1−49*x2)/(7*x)

Final Answer

tan(arccos(7*x))=√(,1−49*x2)/(7*x)

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