Question

Sin4x cos2x+cos4x sin2x=0

Answer 1

Sin4x cos2x + cos4x sin2x = 0
sin(4x+2x)=0
sinx6x=0
6x=pn
x=pn/6

Answer 2

To solve the equation sin(4x) cos(2x) + cos(4x) sin(2x) = 0, we can use trigonometric identities to simplify the equation.

Let's start by using the identity for the sine of a sum:

sin(A + B) = sin(A) cos(B) + cos(A) sin(B)

Applying this identity to the equation, we get:

sin(4x + 2x) = 0

Simplifying further:

sin(6x) = 0

Now, to find the values of x that satisfy this equation, we need to determine when the sine of 6x is equal to zero. The sine function is zero at multiples of π, so we can write:

6x = nπ

where n is an integer.

Solving for x:

x = nπ / 6

Therefore, the general solution to the equation sin(4x) cos(2x) + cos(4x) sin(2x) = 0 is:

x = nπ / 6

where n is an integer.