Simplify (1-cos(2x))/(sin(2x))

Problem

(1−cos(2*x))/sin(2*x)

Solution

1. Apply double angle identities for both the numerator and the denominator.

2. Substitute cos(2*x)=1−2*sin2(x) into the numerator to eliminate the constant term.

3. Substitute sin(2*x)=2*sin(x)*cos(x) into the denominator.

4. Simplify the numerator by performing the subtraction.

1−(1−2*sin2(x))=2*sin2(x)

5. Rewrite the entire fraction using the substituted expressions.

(2*sin2(x))/(2*sin(x)*cos(x))

6. Cancel the common factors of 2 and sin(x) from the numerator and denominator.

sin(x)/cos(x)

7. Identify the resulting expression as the tangent function.

tan(x)

Final Answer

(1−cos(2*x))/sin(2*x)=tan(x)

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