Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sinxsec\frac{x}{t}anx& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}ceins^2x \cdot \frac{x}{t}anx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ceins^2x^2}{t}anx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{aceins^2x^2}{t}nx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{acein^2s^2x^2}{t}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{acein^2s^2x^3}{t}\end{aligned} $$ | |
| ① | $$ s i n x s e c = c e i n s^{1 + 1} x = c e i n s^2 x $$ |
| ② | Multiply $ceins^2x$ by $ \dfrac{x}{t} $ to get $ \dfrac{ ceins^2x^2 }{ t } $. Step 1: Write $ ceins^2x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} ceins^2x \cdot \frac{x}{t} & \xlongequal{\text{Step 1}} \frac{ceins^2x}{\color{red}{1}} \cdot \frac{x}{t} \xlongequal{\text{Step 2}} \frac{ ceins^2x \cdot x }{ 1 \cdot t } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ ceins^2x^2 }{ t } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{ceins^2x^2}{t} $ by $ a $ to get $ \dfrac{ aceins^2x^2 }{ 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. $$ \begin{aligned} \frac{ceins^2x^2}{t} \cdot a & \xlongequal{\text{Step 1}} \frac{ceins^2x^2}{t} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ ceins^2x^2 \cdot a }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ aceins^2x^2 }{ t } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{aceins^2x^2}{t} $ by $ n $ to get $ \dfrac{ acein^2s^2x^2 }{ 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. $$ \begin{aligned} \frac{aceins^2x^2}{t} \cdot n & \xlongequal{\text{Step 1}} \frac{aceins^2x^2}{t} \cdot \frac{n}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ aceins^2x^2 \cdot n }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acein^2s^2x^2 }{ t } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{acein^2s^2x^2}{t} $ by $ x $ to get $ \dfrac{ acein^2s^2x^3 }{ 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. $$ \begin{aligned} \frac{acein^2s^2x^2}{t} \cdot x & \xlongequal{\text{Step 1}} \frac{acein^2s^2x^2}{t} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ acein^2s^2x^2 \cdot x }{ t \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ acein^2s^2x^3 }{ t } \end{aligned} $$ |