Solving Trigonometic Equations
solve for x and give the answers as a equations : ( by radian)
1)cos(sinx)=1
<<<and thanks >>>
We know sin 2x = 2(sinx)(cosx)
so (sinx)(cos)=1/2(sin 2x)
So we can change your equation from
(sinx)(cosx)=1 to
1/2(sin 2x) = 1
(sin 2x) = 2
But the sine value of any angle is between -1 and 1, so your equation has no real solution.
Thanks
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.