$$sec\dfrac{x}{t}anx=\dfrac{acensx^2}{t}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sec\frac{x}{t}anx& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{cesx}{t}anx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{acesx}{t}nx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{acensx}{t}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{acensx^2}{t}\end{aligned} $$ | |
| ① | Multiply $ces$ by $ \dfrac{x}{t} $ to get $ \dfrac{ cesx }{ t } $. Step 1: Write $ ces $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} ces \cdot \frac{x}{t} & \xlongequal{\text{Step 1}} \frac{ces}{\color{red}{1}} \cdot \frac{x}{t} \xlongequal{\text{Step 2}} \frac{ ces \cdot x }{ 1 \cdot t } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ cesx }{ t } \end{aligned} $$ |
| ② | Multiply $ \dfrac{cesx}{t} $ by $ a $ to get $ \dfrac{ acesx }{ t } $. Step 1: Write $ a $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{cesx}{t} \cdot a & \xlongequal{\text{Step 1}} \frac{cesx}{t} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ cesx \cdot a }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acesx }{ t } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{acesx}{t} $ by $ n $ to get $ \dfrac{ acensx }{ t } $. 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. $$ \begin{aligned} \frac{acesx}{t} \cdot n & \xlongequal{\text{Step 1}} \frac{acesx}{t} \cdot \frac{n}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ acesx \cdot n }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acensx }{ t } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{acensx}{t} $ by $ x $ to get $ \dfrac{ acensx^2 }{ t } $. 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. $$ \begin{aligned} \frac{acensx}{t} \cdot x & \xlongequal{\text{Step 1}} \frac{acensx}{t} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ acensx \cdot x }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acensx^2 }{ t } \end{aligned} $$ |