To solve this equation, we can use the double angle identity for cosine.
The double angle identity for cosine states that: cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1
So, we have:cos(x)cos(x) + cos(x)sin(x) = 0cos^2(x) + sin(x)cos(x) = 0cos^2(x) + (1 - cos^2(x)) = 02cos^2(x) - 1 = 02cos^2(x) = 1cos^2(x) = 1/2cos(x) = ±√(1/2)cos(x) = ±1/√2
Therefore, the solutions are:x = π/4 + 2πn or x = 3π/4 + 2πn where n is an integer.
To solve this equation, we can use the double angle identity for cosine.
The double angle identity for cosine states that: cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1
So, we have:
cos(x)cos(x) + cos(x)sin(x) = 0
cos^2(x) + sin(x)cos(x) = 0
cos^2(x) + (1 - cos^2(x)) = 0
2cos^2(x) - 1 = 0
2cos^2(x) = 1
cos^2(x) = 1/2
cos(x) = ±√(1/2)
cos(x) = ±1/√2
Therefore, the solutions are:
x = π/4 + 2πn or x = 3π/4 + 2πn where n is an integer.