Solve for x sin(x)^2-cos(x)^2=0

Problem

sin(x)−cos(x)=0

Solution

1. Identify the trigonometric identity for the difference of squares of sine and cosine, which is related to the double angle formula for cosine: cos(2*x)=cos(x)−sin(x)

2. Rewrite the equation by multiplying both sides by −1 to match the identity.

−(sin(x)−cos(x))=−0

cos(x)−sin(x)=0

3. Substitute the double angle identity into the equation.

cos(2*x)=0

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

2*x=π/2+n*π

5. Isolate x by dividing both sides by 2 where n is any integer.

x=π/4+(n*π)/2

Final Answer

sin(x)−cos(x)=0⇒x=π/4+(n*π)/2

Want more problems? Check here!