sinxcosx=0,x=?

for the problem:

sin(x) * cos(x) = 0
What values of x will result in cos(x)=0 or sin(x)=0?
Hint: in the domain of 0<=x<(2*pi), there are 4 values.

simplify the trigonometric expression.

1 1
--- = ---
1+sin 1-sin

someone please helpp meee!!

To solve the equation sin(x)cos(x) = 0 and find the value(s) of x, we need to determine the values of x for which either sin(x) = 0 or cos(x) = 0.

1. Case 1: sin(x) = 0
The sine function is equal to 0 at specific values of x. These values can be found on the unit circle or by using the properties of the sine function:
- When x = 0 degrees or x = 180 degrees, sin(x) = 0.
- Additionally, sine is a periodic function with a period of 360 degrees. Therefore, x can also be expressed as x = 0 + 360k, where k is an integer (e.g., x = 360, 720, -360, -720, etc.). This will satisfy sin(x) = 0.

2. Case 2: cos(x) = 0
Similarly, the cosine function is equal to 0 at specific angles:
- When x = 90 degrees or x = 270 degrees, cos(x) = 0.
- Cosine is also a periodic function with a period of 360 degrees. Hence, x can be represented as x = 90 + 360k or x = 270 + 360k, where k is an integer.

Combining both cases, the values of x that satisfy sin(x)cos(x) = 0 are:
- x = 0 degrees + 360k
- x = 180 degrees + 360k
- x = 90 degrees + 360k
- x = 270 degrees + 360k

where k is an integer. These values cover all possible solutions for the given equation.