Indian l Olympiad Math Trigonometry Problem l find all possible solutions

Indian l Olympiad Math Trigonometry Problem l find all possible solutions #maths #matholympics #mathproblem #mathstricks #mathoperation #education #mathviral #trignomentry

[jatabhatta]

Your step by step explanation portrays the beauty of Maths. Excellent job.

[YadneshChopde-xshf]

It's so simple
Sin²x = 1-Cos²x
Make quadratic and solve 👍

[sulimanad]

If the answers are sinx=0 OR sinx=1 OR sinx=-1, then any x=½kπ will correspond to the correct answer. There is no need for four different solutions. Lastly, thank you, your explanation is great.

[pranayaniroula]

Thank you for making the solution look so simple.

[All_sci_zone]

I solved this in just 14 steps in less than 3 minutes

[PawanMeena-pm]

Put x equals to zero which satisfies the equation So, the answer is x equals to zero.This is only particular solution. Similarly, pi over 2 is also a particular solution.

[jjjplan]

Assign sinx = 0, ±1 on the complex plane, and every additional right angle starting from 0 will fulfill one of the values. Therefore we can simplify the solution as "x = ±kπ/2"

[oahuhawaii]

7^cos²(x) + 7^sin²(x) = 8 { Use sin²(x) = 1 - cos²(x) }
7^cos²(x) + 7^(1 - cos²(x)) = 8
Let y = 7^cos²(x) ---> cos(x) = ±√log₇(y)
y + 7/y = 8
y² - 8*y + 7 = 0
(y - 1)*(y - 7) = 0
y = 1, 7
cos(x) = ±√log₇(1), ±√log₇(7)
= ±√0, ±√1
cos(x) = 0, ±1
x = k*π/2, k integer

[JJk_edits-by]

Nice solution but music is loud and distracting.

[abhijitbhattacharya]

Simpler way is a = 7^cos^2x
and sin^2x = 1 - cos^2x
This gives a^2-8a+7=0

[tenton]

Anybody attempting olympiad problem should be able to proceed faster. This is excruciatingly slow.

[himadrikhanra]

7/7 sin^2 (x ) + 7 sin ^2 ( x) = 8
Sin^2 ( x) = 1
X = n pi ( n= 1/2, 3/2, 5/2 = ( m + 1)/2 & (m] any even integer [ ) ?

[nirmalbatra]

The sol is so simple but he is doing complicated

[habeebalbarghothy]

It's very clear that 7 + 1 = 8
So x = 90 or 0

[SsSs-bw]

sin²x + cos²x= 1 🤔

1.sin²x=1, cos²x=0
sinx=1, sinx= -1, cos²x=0

2. sin²x=0, cos²x=1
sinx=0, cosx=1, cosx=-1

3. sin²x=0, 5 cos²x=0, 5
sinx=cosx
x= п/4,
п/4=45° ==> corner balance !!

[g.k.]

Unnecessarily u have increased the steps.

[АлексейБигвава]

Приветствую автора. Не стоит применять одну и ту же переменную для замены. Это может привести к путанице.

[satrajitghosh]

writing z for 7 ^ ( sin^2 ( x) ) one gets
7 ^ ( cos^2 ( x) )
= 7 / ( 7 ^ ( sin^2 ( x) ) )
= 7 / z
Hereby z + 7 / z = 8
z^2 - 8 z + 7 = 0
z = 4 + 3, 4 - 3
7 ^ ( sin^2 ( x)) = z = 7 ^ 1, 7 ^0
Hereby, sin^2 ( x) = 1, 0
sin( x) = - 1, 0, 1
x = n π, ( n + 1/2) π
or x = m π /2, for integral m

[rohitsharmarohitsharma]

Background sound distract 😕😕 kar raha hhh

[이규령-jp]

Hopefully you would use, (comma) carefully. Comma means and, so x-1=0, x-7=0 is not proper expression. X-1=0 or x-7=0 would be correct. Mathematics is always related with logics, so 'and' and 'or' must be used correctly.