(cos(frac (1pi )/(2)-1)-cos(2pi -1))(tan(pi +t))=

To solve this expression, we need to simplify the numerator and denominator separately.In the numerator, we have two cosine functions. Let's simplify them one by one.The first cosine function is . We can use the co-function identity for cosine and sine to simplify this expression. The co-function identity states that . Applying this identity, we get: The second cosine function is . We can use the periodic property of cosine to simplify this expression. The periodic property states that . Applying this property, we get: Now, let's simplify the numerator by substituting the simplified expressions for the cosine functions: In the denominator, we have the tangent function. We can use the periodic property of tangent to simplify this expression. The periodic property states that . Applying this property, we get: Now, let's simplify the entire expression by substituting the simplified expressions for the numerator and denominator: This is the simplified form of the given expression.