Problem no 7 Based on Inverse Hyperbolic Function

TL;DR

This video explains how to prove the result of a tan inverse equation using inverse hyperbolic functions.

Transcript

click the bell icon to get latest videos from equator hello students so after covering many problems on inverse hyperbolic function I am going to start with a fresh problem on the same concept so you will see how to prove the result by using the different formulae of inverse hyperbolic function so now here we have to show that tan inverse of I X mi... Read More

Key Insights

• 😇 The video focuses on proving the result of a tan inverse equation using inverse hyperbolic functions.
• 😇 Euler's formula for tan theta is applied to introduce exponential terms and simplify the equation.
• 🚫 The concept of component and dividend oh is used to eliminate variables and obtain the desired result.

Questions & Answers

Q: How is the result of the tan inverse equation proven using inverse hyperbolic functions?

The result is proven by assuming a variable theta, applying Euler's formula for tan theta, and using component and dividend oh to eliminate variables and simplify the equation.

Q: Why is it necessary to use inverse hyperbolic functions in this proof?

Inverse hyperbolic functions are used because the original equation does not have any inverse hyperbolic terms, but their formulas are required to simplify and solve the equation.

Q: Can the result be proven using other methods?

Yes, there are other methods available to prove the result of the tan inverse equation. The method shown in the video is one approach, but alternative methods can also yield the same result.

Q: How can this knowledge be applied in engineering mathematics?

Understanding how to prove equations using inverse hyperbolic functions can be beneficial in solving complex mathematical problems encountered in engineering mathematics.

Summary & Key Takeaways

• The video discusses the process of proving that tan inverse of (ix-a)/(x+a) is equal to (i/2) log(x/a) using inverse hyperbolic functions.

• The solution involves assuming a variable, applying Euler's formula for tan theta, and using the concept of component and dividend oh to eliminate variables.

• The result is proven by demonstrating that the assumed variable theta is equal to (i/2) log(x/a).