Question

Sin^3x-cos^3x=sin^2x-cos^2x

Answer 1

///////////////////////////////////////////////////

Answer 2

To solve the equation sin^3x - cos^3x = sin^2x - cos^2x, we can simplify it using trigonometric identities.

Let's start by applying the identity sin^2x + cos^2x = 1:

sin^3x - cos^3x = sin^2x - cos^2x (sin^2x - cos^2x)(sinx + cosx) = sin^2x - cos^2x

Now, we have sin^2x - cos^2x on both sides of the equation. We can cancel out this common factor:

sinx + cosx = 1

This is the simplified equation after canceling out sin^2x - cos^2x. From here, you can solve for x using various methods such as substitution or graphical analysis.

Please note that this solution assumes the equation holds for all values of x. If there are any specific constraints or ranges for x given in the problem, they should be taken into account while solving.