$$ i s i n = i^{1 + 1} n s = i^2 n s $$

Multiply $qrst$ by $ \dfrac{5}{2} $ to get $ \dfrac{ 5qrst }{ 2 } $.

Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} qrst \cdot \frac{5}{2} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{5}{2} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 5 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5qrst }{ 2 } \end{aligned} $$

Multiply $ \dfrac{5qrst}{2} $ by $ cos+i^2ns $ to get $ \dfrac{5i^2nqrs^2t+5coqrs^2t}{2} $.

Step 1: Write $ cos+i^2ns $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5qrst}{2} \cdot cos+i^2ns & \xlongequal{\text{Step 1}} \frac{5qrst}{2} \cdot \frac{cos+i^2ns}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5qrst \cdot \left( cos+i^2ns \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5coqrs^2t+5i^2nqrs^2t }{ 2 } = \frac{5i^2nqrs^2t+5coqrs^2t}{2} \end{aligned} $$

Add $ \dfrac{-1}{2} $ and $ \dfrac{5i^2nqrs^2t+5coqrs^2t}{2} $ to get $ \dfrac{5i^2nqrs^2t+5coqrs^2t-1}{2} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-1}{2} + \frac{5i^2nqrs^2t+5coqrs^2t}{2} & = \frac{-1}{\color{blue}{2}} + \frac{5i^2nqrs^2t+5coqrs^2t}{\color{blue}{2}} = \\[1ex] &=\frac{ -1 + \left( 5i^2nqrs^2t+5coqrs^2t \right) }{ \color{blue}{ 2 }}= \frac{5i^2nqrs^2t+5coqrs^2t-1}{2} \end{aligned} $$