The identity equation in this problem is (cosx)^2 = (1 + cos2x)/2. This is an identity equation because it is true for all values of x.
The purpose of solving this identity question is to demonstrate the use of trigonometric identities and to practice solving equations involving trigonometric functions.
The steps to solve this identity question are:1. Expand the right side of the equation using the double angle formula for cosine.2. Combine like terms.3. Subtract (cosx)^2 from both sides of the equation.4. Simplify the left side of the equation.5. Divide both sides by 2.6. Take the square root of both sides.7. Simplify the right side of the equation.8. Set the two sides equal to each other to find the solutions for x.9. Check the solutions by plugging them back into the original equation.
The possible solutions for this identity question are all real numbers, since the equation is an identity and is true for all values of x.
Some tips for solving this identity question are:- Familiarize yourself with trigonometric identities and their corresponding double angle formulas.- Make sure to expand the right side of the equation before combining like terms.- Remember to check your solutions by plugging them back into the original equation.- Keep in mind that this is an identity equation, so all values of x will be solutions.