To solve the trigonometric equation (cos(sinx) = 1) in radians, we can follow these steps:
Step 1: Let's use the identity sin(2x) = 2sin(x)cos(x). Applying this identity to our equation, we have:
cos(sin(x)) = 1/2(sin(2x))
Step 2: Now, we can rewrite the equation as:
1/2(sin(2x)) = 1
Step 3: From here, we can solve for sin(2x) by multiplying both sides of the equation by 2:
sin(2x) = 2
Step 4: However, the sine function only takes values between -1 and 1. Therefore, sin(2x) cannot be equal to 2, which means there are no real solutions to the equation cos(sinx) = 1 in radians.
In summary, the equation cos(sinx) = 1 has no real solutions in radians.