3 sec x + 3 tan x = 3

Sure, let's solve the equation step by step:

1. First, let's rewrite the equation: 3 sec x + 3 tan x = 3

2. Divide the entire equation by 3 to simplify: sec x + tan x = 1

3. Now, let's express sec x and tan x in terms of sin x and cos x: 1/cos x + sin x/cos x = 1

4. This simplifies to: (1 + sin x) / cos x = 1

5. Cross multiply to get rid of the denominator: 1 + sin x = cos x

6. Rearrange the equation to isolate sin x: sin x = cos x - 1

7. Now, we know that sin^2 x + cos^2 x = 1. So, we can express cos x as sqrt(1 - sin^2 x) and substitute this into our equation: sin x = sqrt(1 - sin^2 x) - 1

8. Square both sides to get rid of the square root: sin^2 x = 1 - sin^2 x - 2sin x + 1

9. Simplify to get a quadratic equation in terms of sin x: 2sin^2 x + 2sin x - 2 = 0

10. Divide the entire equation by 2 to simplify: sin^2 x + sin x - 1 = 0

11. Now, you can solve this quadratic equation for sin x using the quadratic formula: sin x = [-1 ± sqrt((1)^2 - 4(1)(-1))] / 2(1)

12. Simplify to get the solutions for sin x: sin x = [-1 ± sqrt(5)] / 2

13. Now, you can find the solutions for x using the arcsin function: x = arcsin([-1 ± sqrt(5)] / 2)

Please note that the solutions for x will depend on the domain of the original equation. If the domain is not specified, the solutions for x could be any values that satisfy the equation.