Inverse trig question (1 Viewer)

hs17

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Solve the following equation

sin^-1 (x) - cos^-1 (x) = sin^-1 (3x+1)
 

Qeru

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Solve the following equation

sin^-1 (x) - cos^-1 (x) = sin^-1 (3x+1)
Its always a good idea to state the domain for x before solving so: and .

Now take the sin of both sides to obtain:




Note that: and by the pythagorean identities, we only have to take the positive case here since

Therefore:












But so the only solution is:
 
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idkkdi

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Its always a good idea to state the domain for x before solving so: and .

Now take the sin of both sides to obtain:




Note that: and by the pythagorean identities, we only have to take the positive case here since

Therefore:












But so the only solution is:
In case anyone does not see through why this part of the step is true:

It's because of the domains of inverse trig functions.

Though that solution is a bit long lol.


Obviously:

Trivially, the equation is equivalent to:

Therefore,
 
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Qeru

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In case anyone does not see through why this part of the step is true:

It's because of the domain's of inverse trig functions.

Though that solution is a bit long lol.




[/TEX]
You cant assume without proof. Nor can you assume
 

Qeru

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is this actually not assumable. it's so trivial.
Both results need the double angle formula which is similar to what I did so will result in the same length of working.
 

idkkdi

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Only things you can assume are basic definitions and axioms and results that are on the data sheet (like )
this is why real men take BOS Trials. Screw HSC.
 

idkkdi

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Yeah u need double angle then 'draw a triangle,?' Prove without double angle?
bruh draw a triangle, its so obvious that sin inverse + cos inverse x = 90 degrees it's not even funny.
as for that:
pi/2 = inverse sin + inverse cos same thing.
 

Trebla

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this is why real men take BOS Trials. Screw HSC.
FYI we mark the BoS trials in similar way to HSC lol. You can’t just assume results like that without proof, otherwise you can argue the result you’re trying to prove in the first place is also “trivial”.
 

idkkdi

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FYI we mark the BoS trials in similar way to HSC lol. You can’t just assume results like that without proof, otherwise you can argue the result you’re trying to prove in the first place is also “trivial”.
ur trolling.
inverse sin + inverse cos = pi/2 is like by definition basically.
is this assuming?
 

vernburn

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FYI we mark the BoS trials in similar way to HSC lol. You can’t just assume results like that without proof, otherwise you can argue the result you’re trying to prove in the first place is also “trivial”.
Daily struggles of a 4U kid....
 

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