This equation can be simplified by using trigonometric identities.
The identity we can use is sin^2(x) + cos^2(x) = 1
Therefore, we can rewrite the equation as:
6sin^2(x) + sin(x)cos(x) - cos^2(x) = 0
Using the identity above, we can rewrite it as:
6(1 - cos^2(x)) + sin(x)cos(x) - cos^2(x) = 0
Expanding and simplifying:
6 - 6cos^2(x) + sin(x)cos(x) - cos^2(x) = 0
Rearranging terms:
6 - 7cos^2(x) + sin(x)cos(x) = 0
Therefore, the simplified form of the equation is:
7cos^2(x) - sin(x)cos(x) - 6 = 0
I hope this helps! Let me know if you have any further questions.
This equation can be simplified by using trigonometric identities.
The identity we can use is sin^2(x) + cos^2(x) = 1
Therefore, we can rewrite the equation as:
6sin^2(x) + sin(x)cos(x) - cos^2(x) = 0
Using the identity above, we can rewrite it as:
6(1 - cos^2(x)) + sin(x)cos(x) - cos^2(x) = 0
Expanding and simplifying:
6 - 6cos^2(x) + sin(x)cos(x) - cos^2(x) = 0
Rearranging terms:
6 - 7cos^2(x) + sin(x)cos(x) = 0
Therefore, the simplified form of the equation is:
7cos^2(x) - sin(x)cos(x) - 6 = 0
I hope this helps! Let me know if you have any further questions.