Point out my error pls. (Conditional Trigonometric Identities)

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[livid current]

Pls ping me when replying

[vale forum]

what is the question here?

are you meant to prove something?

[livid current]

Yes.
If: A+B+C=π
Prove that Sin²2A+sin²2B+sin²2C = ...

The R.H.S is incorrect in the question
It fails Value in LHS and Value in RHS when I substitute values of A, B, C ; a+b+c=π

[vale forum]

hmm

i will check it out

[livid current]

ok

[vale forum]

such a weird question

there must be a geometric proof

[dense orchid]

A,B,C are angles of a triangle

[vale forum]

there is no solid geometric proof however

[livid current]

@vale forum
@dense orchid
It is meant to be solved the same way as other Conditional Trigonometric Identities

But this one doesn't satisfy RHS and LHS when I substitute random values that sum to 180°

[vale forum]

[livid current]

Here's another way

[livid current]

It gives me the same result but when I substitute values such that A+B+C=180°

LHS≠RHS

[vale forum]

how does it not solve

???

[livid current]

??

[vale forum]

i think you’re wrong

it subisitutes correctly

[marble sand]

cos(2A+2B) should equal cos(2C) if A+B+C is 180?

[vale forum]

check the pair (90,45,45)

[marble sand]

i’m not sure what the question is

i just read your working on the paper

[livid current]

2A+2B+2C=2π
2A+2B = 2π-2C
cos(2A+2B)=cos(2π-2c)=> ....

[marble sand]

which equals cos(2C)

[livid current]

I misunderstand 2π as 180 😭😭😭😭

[marble sand]

cos is an even function

[marble sand]

oh

[vale forum]

star

[livid current]

I forgot :(
Cos is +ve in 4th quad.

[vale forum]

your solution is correct

[livid current]

but my first step is incorrect :(

[vale forum]

i’m plugging in values

and they wrk

[livid current]

It works for certain values

Like 0,0,180 or something

but not all

[vale forum]

i tried (30,60,90)

[livid current]

I'll resolve it using cos(2A+2B)=Cos2C

Then I'll be back

[livid current]

sin²(2A)+sin²(2B)+sin²(2C)=2[1-cos(2A)cos(2B)cos(2C)] ; [A+B+C=π rad]

Finally solved ✅