y= 5 sin⁡x + 2 cos⁡x

To solve the equation y = 5 sin(x) + 2 cos(x), we can use trigonometric identities and properties. Here are the steps to solve it:

Step 1: Rearrange the equation to separate the sine and cosine terms: y = 5 sin(x) + 2 cos(x)

Step 2: Use the identity sin(x) = cos(π/2 - x) to rewrite the equation: y = 5 sin(x) + 2 cos(x) = 5 cos(π/2 - x) + 2 cos(x)

Step 3: Combine the cosine terms: y = 5 cos(π/2 - x) + 2 cos(x) = 5 cos(π/2)cos(x) + 5 sin(π/2)sin(x) + 2 cos(x) = 5(0)cos(x) + 5(1)sin(x) + 2 cos(x) = 5 sin(x) + 2 cos(x)

Step 4: Simplify the equation: y = 5 sin(x) + 2 cos(x)

So, the equation y = 5 sin(x) + 2 cos(x) remains the same after simplification.