how to solve this trigonometric equation from another one | Summary and Q&A

TL;DR

Learn how to solve trigonometric equations involving secant x, tangent x, cosecant x, and cotangent x.

Key Insights

• ☺️ The reciprocal relationship between tangent x and cotangent x can be useful in solving trigonometric equations.
• 😑 Multiplying equations by variables can help simplify expressions and showcase relationships between terms.
• 🧑‍🏭 Cancelling out common factors can make equations more manageable and easier to solve.

Transcript

okay that's to summer for fun here we're gonna find out if secant X plus tangent X is equal to fifteen over seven then what's the value for cosecant X plus cotangent X of course please pause the video and try this first okay hopefully gets up a chance to try it and I will write down the answer right here for you guys the answer to this right here i... Read More

Questions & Answers

Q: How did the speaker approach solving the trigonometric equation?

The speaker multiplied both sides of the equation by K, a variable, to get a number to work with. Then, they multiplied out the equation using sine and cosine functions to simplify the expression.

Q: How did the speaker utilize the reciprocal relationship between tangent x and cotangent x?

The speaker recognized that tangent x and cotangent x are reciprocals of each other. By multiplying the equation by K, they were able to utilize this relationship to simplify the expression.

Q: What steps did the speaker take to solve the equation after multiplying out the terms?

The speaker subtracted the terms involving 1 over cosine x and 1 over sine x from the equation. This allowed them to simplify the expression and eliminate these terms.

Q: How did the speaker arrive at the final answer of eleven over four?

By simplifying the expression further and canceling out common factors, the speaker arrived at the equation 22 over 7 equals 8 over 7K. Simplifying this equation, they found K to be equal to eleven over four.

Summary & Key Takeaways

• The video explains how to solve the equation secant x plus tangent x equals fifteen over seven, and find the value for cosecant x plus cotangent x.

• The speaker utilizes equations and algebraic manipulation to simplify the problem.

• The final answer to the equation is eleven over four.