3sinx+7cosx=-1

To solve the equation 3sin(x) + 7cos(x) = -1, we can rewrite it using the identity sin(x) = cos(π/2 - x):

3sin(x) + 7cos(x) = -1 3cos(π/2 - x) + 7cos(x) = -1

Expanding the equation:

3cos(π/2)cos(x) + 3sin(π/2)sin(x) + 7cos(x) = -1 0 + 3sin(x) + 7cos(x) = -1

Rearranging the terms:

3sin(x) + 7cos(x) + 1 = 0

Now, we can solve this equation using trigonometric identities and techniques.