In this discussion, we are going to verify trig identities using the fundamental trig identities.
Here is an outline of this discussion:
- Review of the Fundamental Trig Identities
- Verify that sinx*tanx + cosx = secx
- Verify that sinx/(1+cosx) = cscx -cotx
Let’s begin!
Review of the Fundamental Trig Identities
Here is a quick refresher of the fundamental Trigonometric Identitie.
Now we are ready to verify our trig identities.
Verify that sinx*tanx + cosx = secx
Let us look at our first example. We want to show that
sinx*tanx + cosx = secx
We begin with the left-hand side (LHS) and work our way to the right-hand side (RHS).
LHS
= sinx*tanx + cosx
= sinx*sinx/cosx + cosx Using quotient identity
=sin^2x / cosx + cosx
=sin^2x / cosx + cos^2x / cosx Getting a common denominator
=(sin^2x + cos^2x) / cosx Combine the numerator
=1/cosx Using a Pythagorean Identity
= secx Using a reciprocal Identity
= RHS
Since the left-hand side is equal to the right-hand side, the identity is verified.
Verify that sinx/(1+cosx) = cscx -cotx
Next we want to verify that
sinx/(1+cosx) = cscx -cotx
We begin with the left-hand side (LHS) and work or way to the right-hand side (RHS).
LHS
= sinx/(1+cosx)
=(sinx)(1-cosx)/(1+cosx)(1-cosx) Multiplying top and bottom by (1-cosx)
=
(sinx)(1-cosx)/(1-cos^2x)
=
(sinx)*(1-cosx)/(sin^2x) since 1-cos^2x =sin^2x
=
(1-cosx)/(sinx) Canceling common factors
1/sinx -cos/sinx Separating the numerator
cscx -cotx Using a reciprocal and quotient identity
= RHS
Since the left-hand side is equal to the right-hand side, the identity is verified.
That is how we verify trig identities!
Thank you for reading!
I hope that I can assist you on your math journey!
Sincerely,
MathAngel369
🔑 Math Course:
Practice is the key! If you would like to become an expert in trig identities, consider taking my math course.
My courses include:
1. Videos and Articles
2. Practice Problems with the Answer Key
3. Quizzes with the Answer Key
4. Hand Written Notes discussing an overview and concepts that I use to teach my college students
5. Hand Written notes with extra problems solved, showing every step.
6. Certificate of Completion
7. 30 day Money Back Guarantee
And much more!
You can preview about 10 minutes of the course for free before purchasing.
Here is the link to my math course:
Proving/Verifying and Using Trig Identities
For a list of all my courses, go to my website: