Verify the Identity sin(x)^2-cos(x)^2=0

Problem

sin2(x)−cos2(x)=0

Solution

1. Identify the expression as a trigonometric equation to be solved or an identity to be verified for specific values of x

2. Apply the double angle identity for cosine, which states cos(2*x)=cos2(x)−sin2(x)

3. Rewrite the left side of the equation by factoring out a negative sign to match the identity.

−(cos2(x)−sin2(x))=0

4. Substitute the identity cos(2*x) into the equation.

−cos(2*x)=0

5. Simplify by multiplying both sides by −1

cos(2*x)=0

6. Solve for 2*x by finding where the cosine function equals zero.

2*x=π/2+n*π

7. Isolate x by dividing by 2

x=π/4+(n*π)/2

Final Answer

sin2(x)−cos2(x)=0⇒x=π/4+(n*π)/2

Want more problems? Check here!