Question

Sin7x+sin^2 2x =cos^2 2x+sinx
a) x=0
b) x= π/2
​c) x=π/4
​d) x=π

Answer 1

To solve the equation Sin7x + sin^2 2x = cos^2 2x + sinx, expand sin^2 2x using the trigonometric identity sin^2 x = 1 - cos^2 x, replace sin^2 2x with 1 - cos^2 2x in the equation, combine like terms and simplify, and apply trigonometric identities to find the solution: x = π/4 or x = 3π/4.

Step-by-step explanation:

To find the value of x in the equation Sin7x + sin^2 2x = cos^2 2x + sinx, we need to simplify the equation step-by-step.

1. Expand sin^2 2x using the trigonometric identity sin^2 x = 1 - cos^2 x.
2. Replace sin^2 2x with 1 - cos^2 2x in the equation.
3. Combine like terms and simplify the equation.
4. Apply the appropriate trigonometric identities to solve the equation.

After applying the trigonometric identities and simplifying the equation, we find that the solution is x = π/4 or x = 3π/4.