Question

Solve sin7x+sin^2 2x =cos^2 2x+sinx
a) x= π/2
b) x=π
c) x= 3π/2
d) x= 2π

Answer 1

There is no specific value of x that satisfies the equation sin7x + sin^2 2x = cos^2 2x + sinx.

Step-by-step explanation:

To solve the equation sin7x + sin^2 2x = cos^2 2x + sinx, we need to simplify and rearrange the equation.

Using trigonometric identities, we can express sin^2 2x and cos^2 2x in terms of sin 2x and cos 2x:

1. sin^2 2x = (1 - cos^2 2x)
2. cos^2 2x = (1 - sin^2 2x)

Substituting these values in the equation and simplifying, we get:

sin7x + sin 2x + sin x = 1

Now, to solve for x, we can use transformations of sinusoidal functions or graphing methods. However, there is no specific solution given in the answer choices (π/2, π, 3π/2, or 2π). Therefore, it is not possible to determine a single value for x that satisfies the equation.