xin (0,(pi )/(2)) (cos(frac (3pi )/(2)-x)-sin(2pi -x))(tan(pi +x))=?

To solve this expression, let's simplify each trigonometric function step by step:1. : - This is the cosine of an angle in the second quadrant. - We can use the identity . - Applying this identity, we get .2. : - This is the sine of an angle in the fourth quadrant. - We can use the identity . - Applying this identity, we get .3. : - This is the tangent of an angle in the third quadrant. - We can use the identity . - Applying this identity, we get .Now, let's substitute these simplified expressions back into the original expression: Simplifying further: We know that , so we can substitute this into the expression: Simplifying the fraction: Expanding the numerator: Now, we can simplify the expression by canceling out common factors: Since , we know that . Therefore, we can simplify further: So, the simplified expression is: This is the final simplified form of the given trigonometric expression.