$$tanx\cdot\dfrac{secx-cosx}{s}inx=\dfrac{acein^2stx^3-acin^2ostx^3}{s}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}tanx \cdot \frac{secx-cosx}{s}inx& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{acenstx^2-acnostx^2}{s}inx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{aceinstx^2-acinostx^2}{s}nx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{acein^2stx^2-acin^2ostx^2}{s}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{acein^2stx^3-acin^2ostx^3}{s}\end{aligned} $$ | |
| ① | Multiply $antx$ by $ \dfrac{cesx-cosx}{s} $ to get $ \dfrac{ acenstx^2-acnostx^2 }{ s } $. Step 1: Write $ antx $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} antx \cdot \frac{cesx-cosx}{s} & \xlongequal{\text{Step 1}} \frac{antx}{\color{red}{1}} \cdot \frac{cesx-cosx}{s} \xlongequal{\text{Step 2}} \frac{ antx \cdot \left( cesx-cosx \right) }{ 1 \cdot s } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acenstx^2-acnostx^2 }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{acenstx^2-acnostx^2}{s} $ by $ i $ to get $ \dfrac{ aceinstx^2-acinostx^2 }{ s } $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{acenstx^2-acnostx^2}{s} \cdot i & \xlongequal{\text{Step 1}} \frac{acenstx^2-acnostx^2}{s} \cdot \frac{i}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( acenstx^2-acnostx^2 \right) \cdot i }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ aceinstx^2-acinostx^2 }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{aceinstx^2-acinostx^2}{s} $ by $ n $ to get $ \dfrac{ acein^2stx^2-acin^2ostx^2 }{ s } $. Step 1: Write $ n $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{aceinstx^2-acinostx^2}{s} \cdot n & \xlongequal{\text{Step 1}} \frac{aceinstx^2-acinostx^2}{s} \cdot \frac{n}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( aceinstx^2-acinostx^2 \right) \cdot n }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ acein^2stx^2-acin^2ostx^2 }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{acein^2stx^2-acin^2ostx^2}{s} $ by $ x $ to get $ \dfrac{ acein^2stx^3-acin^2ostx^3 }{ s } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{acein^2stx^2-acin^2ostx^2}{s} \cdot x & \xlongequal{\text{Step 1}} \frac{acein^2stx^2-acin^2ostx^2}{s} \cdot \frac{x}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( acein^2stx^2-acin^2ostx^2 \right) \cdot x }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ acein^2stx^3-acin^2ostx^3 }{ s } \end{aligned} $$ |