To solve this equation, we can use the identity for the product of two trigonometric functions:
cos(A)cos(B) - sin(A)sin(B) = cos(A + B)
So in this case, we have:
cos(2x)cos(7x) - sin(2x)sin(7x) = cos(2x + 7x)
cos(2x + 7x) = cos(9x)
Now we have:
cos(9x) = -1
To find the solution, we can see that the cosine function equals -1 at odd multiples of π. Therefore, we can write the general solution as:
9x = (2n + 1)π
where n is an integer.
So, the solution to the equation cos(2x)cos(7x) - sin(2x)sin(7x) = -1 is:
x = (2n + 1)π / 9
To solve this equation, we can use the identity for the product of two trigonometric functions:
cos(A)cos(B) - sin(A)sin(B) = cos(A + B)
So in this case, we have:
cos(2x)cos(7x) - sin(2x)sin(7x) = cos(2x + 7x)
cos(2x + 7x) = cos(9x)
Now we have:
cos(9x) = -1
To find the solution, we can see that the cosine function equals -1 at odd multiples of π. Therefore, we can write the general solution as:
9x = (2n + 1)π
where n is an integer.
So, the solution to the equation cos(2x)cos(7x) - sin(2x)sin(7x) = -1 is:
x = (2n + 1)π / 9
where n is an integer.