Your method is unquestionably the best. I showed after a long calculation and by setting y=2x, that the equation sin^2(3x)=sin(2x)sin(6x), is equivalent to (cos(y)-1) (2 cos(y)+ 1) (4 cos^2(y)-3)=0. The solution of the equation 4 cos^2(y)-3=0 then gives y=30° and therefore x=15°. Thank you for this nice exercise !
@yazanmanasrah9924
Жыл бұрын
Nice approach and nice knowledge of trigonometric identities as a pure mathematic major I can’t pass your step when you cancelled sin(x) at 6:58 without proving that it doesn’t equal zero I know it can’t but just my math conscience 😂😂 Other wise it’s perfect 👍🏻
@stevenmurphy2445
Жыл бұрын
an explanation of the trig substitutions would be helpful.
@nehronghamil4352
Жыл бұрын
Although in most trigonometric problems involving triangles, the law of sines is very useful. However I bypassed that by noting the height of both triangles are equal. If the length of the equal line segments is equal to d, then d * sin(2x) is equal to d/2 * tan (3x) or tan(3x)/sin(2x)=2 which can be expressed as 2 cos(3x) * sin(2x)=sin(3x) the form you also arrived at.
@holyshit922
Жыл бұрын
From sum of angles in triangle we can conclude that triangle PSR is isosceles so PS = PR From sine law in triangle PQS we can calculate side lengths of triangle PQS in terms of side PQ Once we have side lengths in triangle PQS we can easily calculate side lengths in triangle PQR From cosine law in triangle PQR we will get cos(4x)=1/2 4x = 60 degree Can 4x equal 300 Not in plane because 3x would be grater than 180 degree so x = 15 degree It would be easier if we somehow can show that line PR is perpendicular to line PS
@liviutatarush1249
Жыл бұрын
It can be solved extremely simply, three equations with three unknowns, the angles x, y and z, where y is SPR and z is QSP. The PSR angle is 180-z. Just arithmetic!
@Cdictator
10 ай бұрын
Enjoyed this. Keep up the good work bro!
@yuusufliibaan1380
Жыл бұрын
Thank you, I got a lot of information from your video. May God bless you 👍❤️
@davidseed2939
Жыл бұрын
i wouldnt have known to approach the problem in that way. i would have tried to get everything in terms of sinx and probably got stuck. How did you know what trig identities to use? but also I notice now that one of the triangles (PSR) is a 90,45,45 triangle which suggests a geometric approach may be possible. EDIT. If you make a copy of PQR such that P' maps to R Q' maps to S and S' ( call it T) is below SR. Join T to P. PTR is an equilateral triangle. each angle 4x. not easy to prove.
@mallikarjun413
Жыл бұрын
Iam a very beginner to geometry, Please don't mind if I was wrong but doesn't the value of the x depend on the value of y? We don't know either x or y. So, 6x+y =180. X varies with y. Please correct me where I went wrong If I was wrong
@KM-om1hm
Жыл бұрын
You just uploaded a nearly same math 2 days ago
@thewarriorclasses
Жыл бұрын
Great sir
@kwakkkk666
Жыл бұрын
I proved that in elementary logical with auxiliary line
@DR-kz9li
Жыл бұрын
I started with external angles, then algebra
@advaykumar9726
Жыл бұрын
(sin3x/sin2x)=(sin6x/sin3x)
@minka866
Жыл бұрын
In this case just trigonometry?
@javiernasser3574
Жыл бұрын
U can also do it with geometry, translating triangles, forming isoceles and using congruent triangles
@idvbane8580
Жыл бұрын
V good explanation 🥰🥰🥰
@MathBooster
Жыл бұрын
Thank you 🙂
@mortezamehraban1990
Жыл бұрын
X=60
@nguyenba
Жыл бұрын
Hình của đề bài thiếu 2 cạnh bằng nhau làm mất thời gian quá.
@DaFlashPro
Жыл бұрын
Can't we just get triangle PQR is isosceles triangle as PQ = SR? We get that Angle PRS = Angle QPR So we get , Angle QPR = 3x. So as the sum of the angles in triangle PQR is 180 degrees. So, 2x + 3x + 3x = 180 8x = 180, x = 180/8 = 22.5. Please tell me if I am mistaken
@delxa270
Жыл бұрын
Nah, PQ is equal to SR, not QR. So you can't assume that triangle PQR is isosceles.
@DaFlashPro
Жыл бұрын
@@delxa270 thanks
@idvbane8580
Жыл бұрын
🥰🥰🥰🥰
@idvbane8580
Жыл бұрын
Math🥰🥰🥰
@chotusingh1940
Жыл бұрын
X=10,20,....solve this
@idvbane8580
Жыл бұрын
Sir🥰🥰🥰
@shorts_for_shortcuts
Жыл бұрын
Why is there a pi
@musicsubicandcebu1774
Жыл бұрын
In trigonometry pi can mean 180 degrees
@shorts_for_shortcuts
Жыл бұрын
@@musicsubicandcebu1774 oh that makes a lot of sense so sin( π-x) = sin180-x
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