Trigonometric Proofs || Pre-Calculus Tutorial || Verifying Trigonometric Identities

Having trouble with Trig Proofs? Yeah don't worry, this stuff is not very intuitive at first glance. Let's see if I can help.

In this video, we'll be looking at 25 different trig proof problems in depth. I want you to see my strategy for solving these problems, and the first thing I always do is sit back and just think about all of the different identities or manipulations I could do with this. Taking a minute to think really helps alleviate the pain of running into dead end after dead end with these types of problems.

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[danielvidal]

The problem at 1:26:23 can be solved a simpler way by letting the cotangent on the top of the numerator be equal to 1/tan(x) rather than cos(x)/sin(x) because then the LHS simplifies to 1/sin(x) + 1/tan(x) on the numerator and you can switch the denominator around to be sin(x) + tan(x). From there, you can make a substitution for a=sin(x) and b=tan(x) to simplify the LHS. The numerator using the formula for adding fractions becomes 1/a + 1/b = a+b/ab. The entire LHS fraction becomes ((a+b)/ab)/(a+b). The numerator and denominator cancel out and just becomes 1/ab which we see is equal to the RHS because they're reciprocal identities on the RHS and (1/a)(1/b) = 1/ab.

It's true that cot(x) = cos(x)/sin(x) because it's the reciprocal of the tan(x), but since it's the reciprocal of tan(x), it is also equal to 1/tan(x) by definition. Sometimes there's less work involved when using 1/(tan(x) instead because we have a 1 on the numerator instead of having it as a ratio of two functions.

[osostexanos]

Thanks for this! Got my midterm tomorrow

[LudusYT]

Just so everyone knows, Calculus 3 Final Review will be the released soon! Below is my to do list for videos; I'll try to do 1-2/week.


1. Multiple Integrals (Calculus 3 Topic)
2. Vector Calculus (Calculus 3 Topic)
3. Calculus 3 Final Review
4. Linear Algebra Final Review
5. Calculus 1 Final Review


P.s. I might redo Calc 2 Final Review with the higher quality setup. What are your thoughts on that?

[annegreek]

Hello there! Can you please help me prove this identity? Please, please 🥺 I have been solving this for 3 days now and I still can't figure it out.

[1+sin (x)+cos (x)] / [1+sin (x)-cos (x)] = [1+cos (x)] / sin (x)

[antoniomele]

Looking forward to the calc 3 final video! We just started the section on double integrals in my class