Proving Trigonometric Identities Grade 12

Proving Trigonometric Identities Grade 12
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[@thembelamathsclub4403]

This structured approach is interesting. Thank you for sharing it.

[@kevinmathscience]

Absolute pleasure :)

[@kvrmvkvziii9490]

Hey Kevin!
What if one was to make the cos(12x) into cos(6x+6x) then expand the compound angle into:
cos6x.cos6x - sin6x.sin6x + sin²(6x)
then by means of like terms one would end up with:
cos²(6x )- sin²(6x)+sin²(6x)
then eventually one will be left with:
cos²(6x)
which is the equivalent of 1-sin²(6x) due to :
•cos²(6x) + sin²(6x) = 1
•cos²(6x)=1-sin²(6x)
Therefore LHS = RHS.

[@kevinmathscience]

Beautiful :) Yes absolutely perfect!!!

[@yoliswanyalungu1619]

Are kevin Smith...the writer of the Math textbook?

[@kevinmathscience]

I get this question a lot :) No I am a different Kevin :)

[@alexandermeyer8404]

Kevin, for the question cos(12x) +sin^2(6x). could we not take the identity of cos^2(6x) - sin^2(6x)? because after wards youd be left with cos^2(6x)-sin^2(6x) + sin^2(6x), which gives you a cos + sin which = 1? then youd have 1 - sin^2(6x) which is the answer?

[@moebarakat5078]

Yeah, I too came to the same conclusion but i think we're correct as well.

[@fudge000]

I'm here for this, thanks Kevin❤

[@zaeemhassen-re4dk]

Kevin is my man😍

[@maxfarouk3407]

Hi sir, for the second question. Would be possible to use the top formula for cos2a.
I think its an extra step to your way but i think it works, im just want to make sure im not making a mistake somewhere.
My thought process was that the RHS 1 - sin^2(6x) = cos^2(6x). So then i make the LHS = cos^2(6x) using the top formula. Is that always a way of doing it?

[@katlegolinky4743]

The best 🙌🏼

[@kevinmathscience]

Thank you Katkego :)

[@AmendaMngwengwe-ci6pt]

Hey Kevin Sir I'm confused in this equation cause I don't know how to deal with 3
Sin3x/1-cos3x = 1+cos3x/sin3x
(/ that's my division sign)

[@zubenathimafilika8742]

Sir kevin what if it was sin12x in question 2

[@soberboyentertainment4695]

hey kevin just wanted to ask in question 2 right the last few steps of the question is it 1-sin squared 6x because of the formula or because when you were minusing the values i got confused wasnt the negative supposed to be -1 sin ...

[@kevinmathscience]

Hello, I changed cos12x into 1-2sin^2(6x) and then we had:
1- 2sin^2(6x) + sin(6x) which then gives 1 - sin^2(6x) if you combine like terms.

[@sc.ndhlovu]

Sir I got confused by the second identity
How does 1-2sin²(6x) + sin²x equal the right hand side ?

[@kevinmathscience]

Hello :) 1-2sin²(6x) + sin²(6x) adds up to 1-sin²(6x) which is RHS

[@sc.ndhlovu]

@@kevinmathscience Thank you , this video has been helpful

[@ona4323]

Sir I’m still confused how does the second step come about where did you get the 1 from

[@kevinmathscience]

From the formula sheet :)

[@naledimokibelo5077]

Kevin help me with these 1 plsss
Cos 2B= 3/5
A) CosB
B)SinB
C)Cos(B+45)

[@kevinmathscience]

Hello Naledi, check this video:ua-cam.com/video/NdIr-_wYmls/v-deo.html

[@sphesobantu8651]

Sir I used a different way which is cos²x -sin²x and still got the same answer as the other method you used .....is it fine?

[@jamesderby2838]

yes it should be fine, there are so many options in trig

[@sphesobantu8651]

@@jamesderby2838 Thank you

[@LuyandaBusani]

🔥