\( \frac { \sin ( 90 - x ) \cdot \sin ( 980 - x ) } { \cos ( 3 + 0 ^ { \circ } - x ) \cdot \sin ( 180 - x ) \cdot \cos 90 - x ) } \)

It seems that the expression is too complex for direct simplification. Let's break it down step by step using trigonometric identities to simplify it manually. The expression is: \[ \frac { \sin ( 90 - x ) \cdot \sin ( 980 - x ) } { \cos ( 3 - x ) \cdot \sin ( 180 - x ) \cdot \cos ( 90 - x ) } \] ### Step 1: Simplify the components 1. **Using the co-function identity**: \[ \sin(90 - x) = \cos(x) \] So, we can replace \(\sin(90 - x)\) with \(\cos(x)\). 2. **For \(\sin(180 - x)\)**: \[ \sin(180 - x) = \sin(x) \] 3. **For \(\cos(90 - x)\)**: \[ \cos(90 - x) = \sin(x) \] ### Step 2: Substitute these identities into the expression Now substituting these identities into the original expression, we get: \[ \frac { \cos(x) \cdot \sin(980 - x) } { \cos(3 - x) \cdot \sin(x) \cdot \sin(x) } \] This simplifies to: \[ \frac { \cos(x) \cdot \sin(980 - x) } { \cos(3 - x) \cdot \sin^2(x) } \] ### Step 3: Final expression Thus, the simplified form of the original expression is: \[ \frac { \cos(x) \cdot \sin(980 - x) } { \cos(3 - x) \cdot \sin^2(x) } \] This is the simplified version of the given expression. If you need further calculations or evaluations, please specify!