Simplify 24 Trigonometric Expressions With Identities

In this video we will explore 24 different trigonometric expressions for to simplify. To Simplify we will use algebraic processes as well as trigonometric identities.
Corrections:
24:13 In Example #20, sec^2x is equal to (tan^2x + 1). So final answer: -5(tanx-secx)
25:15 In Example #21, final answer is cos^2 and not tan^2
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[@wormdeath]

This video saved me, trig identities is one of the hardest things to wrap my head around so this video was a major help! Thank you so much!

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[@wormdeath]

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[@johnarickmedinasyc2546]

@@maheerhuq6708 FACTS

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[@samdwichenjoyer]

Such a cathartic feeling when you're halfway through the vid and you can say the answers before he does. Awesome lesson Mr. McLogan!

[@natesky6603]

I was lost by problem 5

[@jeremybritton7361]

Endless thank you’s go out to you man. Such a great teacher! Keep up the good work man, you always help out tons

[@mathlegendno12]

This is amazing! I have learnt countless amount of things from this channel. Thanks!

[@laneyd1440]

This is all...so above my head. Thanks for the help~

[@tyronegriff841]

Please slow down a little next time. It would also be helpful to include an, "if you are struggling with these concepts review videos a and b." Thanks

[@williamzhong4933]

At 25:21 isn't 1/sec^2 = cos^2 and not tan^2?

[@elijahjohnson3125]

Thought the same thing man

[@timothyallshouse3524]

ya same, i was like wth, then i saw that he was wrong but ya it is cos^2

[@srihariananthalwan4610]

Yea u right I was like wtf is my whole life a lie and then I realized it was just a silly mistake

[@fly4lyf_213]

The reciprocal of sec is cos.

[@amber6329]

This was amazing, thank you! Lots of practice to run through with someone who knows that they're doing. I also got cos^2X for 21, and also didn't understand 22 either. Thanks for the video!

[@maomaozzz]

I also got cos^2theta for #21 I think he made a mistake

[@shahdabbas5843]

how did you distribute number 5?

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[@highstridelease4452]

Thank you 🙏 this helps a lot

[@MathemaTeach]

This is a Precal topic. Great. Thanks 👍👍👍👍

[@MaryJones-dv4tm]

Thanks a lot sir😇😇may God Bless you

[@757Media]

I like what you did here. How did you do this to have it show the problems that you are working behind you. Also where can I find more problem sets to work on and practice

[@rice1549]

Thank you so much ! :)

[@mgthebee7043]

Thank you so much!

[@Anrufen_Fahren_Schneiden_gehen]

Fantastic!

[@Popo-br8xq]

Thank you Mr. McLogan. You saved my math score 🤧

[@markkleinberg]

Is the answer to question 5 correct ? I calculated the answer as (sin^2(x)+1)/(cos^2(x)) and verified it with the Symbolab program

[@dewretoz]

For problem 14 wouldn't the answer be "sin2x+1"? You should be able to simply the 2sinxcox to sin2x due to sine double angle identity. sin2θ = 2sinθcosθ

[@markkleinberg]

It seems that the sign is wrong on the answer to question 20 since sec^2x=tan^2x+1 not tan^2x-1

[@patrickclinton2802]

Thank you.

[@justminri426]

I am truly grateful for this video😭💖Thank you so much! I hope I can answer my exam tomorrow

[@brianmclogan]

You got this!!

[@liofan7266]

Thank you

[@pepmaths5812]

Trig exam the next three hours🇯🇲🇯🇲🇯🇲🇯🇲👍👍i am gonna smash it

[@baslealdereje5369]

thank u very much.. I have much respect but error in 21:- 1/sec2theta is cos2 theta...... with much respect

[@brianmclogan]

Appreciate you letting me know

[@sharshaf2377]

thank you bro

[@johnathanpatrick6118]

Error on #20 -- sec^2(x) = tan^2(x) + 1. Denominator should have been -1, which would make the answer -5(tan(x) - sec(x)), or if you prefer, 5(sec(x) - tan(x)).

[@fly4lyf_213]

I also got -5(tanx - secx) at first. But then, I end up doing what the professor did. So I guess it can be done both ways?

[@johnathanpatrick6118]

@@fly4lyf_213 The negative sign matters here. When you multiply both the numerator and denominator of the expression by tan(x) - sec(x), you get a difference of squares in expanded form, tan^2(x) - sec^2(x). One of the core trig identities is sec^2(x) - tan^2(x) = 1 (the others are sin^2(x) + cos^2(x) = 1 and csc^2(x) - cot^2(x) = 1); if you had this resulting difference of squares you would be correct to not put the negative sign in front of the 5. In order to get tan^2(x) - sec^2(x) on the left you'd have to multiply by -1 and do likewise on the right, meaning tan^2(x) - sec^2(x) = -1. Back to Professor McLogan's work, because the 5 in front of tan(x) - sec(x) is positive, you have positive divided by negative which is negative; that means if you want to keep tan(x) - sec(x) as part of your answer, you must attach the negative in front of the 5. Otherwise, you can distribute the negative and get sec(x) - tan(x) while keeping the 5 positive.

[@kpeacek]

for number 9 cotxcosx can still be simplified can we do cos/sin times cos and we can get rid of cos and get sine as the final answer?

[@Rachel-tu8pq]

he switched up number 24 at the last minute. The answer to the original # 24 is secx !

[@ashleyaby1421]

nawa'y makasurvive sa trigo exam bukas

[@autumnwind2241]

Why the question 24 changed in the end @.@

[@SM-qn7sr]

how is #21, 1/sec^2(theta) = tan^2(theta)?

[@omkarlanghi7787]

Sir in the book identies is (1+tan^2x = sec^2x )

[@akbulutarda472]

in my country csc writes as cosec

[@chelsaroo91]

you da man

[@simonphoenix3789]

i don't get number 2... how does that make sense? how can that sin of pi/2 -x equal cos x?

[@julia-qp1wb]

you may have figured this out by now since you commented this a week ago, but anyway: it’s another set of identities called cofunction identities that include pi/2. find a list of them online, it will make more sense then

[@johnlloydmanimog3042]

24:26 Tan²x - tan²x =1?????

[@ryanwilson9555]

1/sec^2θ ≠ tan^2θ 1/sec^2θ = cos^2θ

[@fakhrulzainal5384]

Amazingg, but didn't understand no. 22

[@kexu3234]

did you made a mistake on number 20? cause i thought sec2x transform to 1+tan2x, can someone explain this to me?

[@brianmclogan]

Could have

[@neilgorias5492]

Thank you 😊

[@markkleinberg]

Shouldn't the answer to Question 21 be cos^2x ?

[@patrickclinton2802]

Yes

[@patrickclinton2802]

Also question 20 is incorrect

[@jimmygore8214]

17:59

[@isaacchen1893]

I think there might be an error with 21.

[@hannajaeger8868]

You're my bestie

[@VarunDoesMaths]

Error at 16:54 , 2sinxcosx = sin2x

[@ismaelmohamed4678]

Problem 21 25:13 Minute its 1/sec^2x and the answer was cos^2x

[@keirakarger6401]

I must just be dumb asf cause how the hell did he just do 3

[@rishavraj374]

21. 1/sec^2x = cos^2x

[@fannyokukamuna8230]

i don't agree with number 17

[@johnathanpatrick6118]

What's wrong with #17?

[@l_Scythe_l]

livestream?

[@l_Scythe_l]

@Asiful Alam Choudhury I meant if he was going to do one

[@JonCom3dy]

Why did KZbin recommend this to me?

[@johnmarkodayan2141]

uhmmm... You never age....

[@Burningarrow7]

#20 is wrong. Sec²x = tan + 1 so the answer ends up -5(tanx - secx) You did another mistake #21 1/sec²x = cos²x not tan²x Silly mistakes they get us all!

[@thatomofolo452]

Let's get it let's go 🚀🥳🤸🏋️⛹️🤾💯💫