Verify the Identity 1-cos(6x)=3sin(2x)

Problem

1−cos(6*x)=3*sin(2*x)

Solution

1. Identify the goal to verify if the equation 1−cos(6*x)=3*sin(2*x) is an identity.

2. Apply the double angle formula for cosine, cos(2*θ)=1−2*sin2(θ) where θ=3*x

3. Substitute the formula into the left side of the equation.

1−cos(6*x)=1−(1−2*sin2(3*x))

4. Simplify the expression by distributing the negative sign.

1−1+2*sin2(3*x)=2*sin2(3*x)

5. Compare the simplified left side 2*sin2(3*x) to the right side 3*sin(2*x)

6. Evaluate specific values to check for equality, such as x=π/6

Left side: *1−cos(π)=1−(−1)=2

Right side: *3*sin(π/3)=3*(√(,3)/2)=(3√(,3))/2

7. Conclude that since 2≠(3√(,3))/2 the equation is not an identity.

Final Answer

1−cos(6*x)≠3*sin(2*x)

Want more problems? Check here!