Inverse trig question (1 Viewer)

hs17

Member
Joined
Mar 1, 2020
Messages
58
Gender
Female
HSC
2021
Solve the following equation

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

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
258
Gender
Male
HSC
2021
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:
 
Last edited:

idkkdi

Well-Known Member
Joined
Aug 2, 2019
Messages
1,444
Gender
Male
HSC
2021
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,
 
Last edited:

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
258
Gender
Male
HSC
2021
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

Well-Known Member
Joined
Dec 30, 2020
Messages
258
Gender
Male
HSC
2021
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

Well-Known Member
Joined
Aug 2, 2019
Messages
1,444
Gender
Male
HSC
2021
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

Well-Known Member
Joined
Aug 2, 2019
Messages
1,444
Gender
Male
HSC
2021
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

Administrator
Administrator
Joined
Feb 16, 2005
Messages
7,191
Gender
Male
HSC
2006
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

Well-Known Member
Joined
Aug 2, 2019
Messages
1,444
Gender
Male
HSC
2021
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

Active Member
Joined
Aug 30, 2019
Messages
157
Location
Vern Gang
Gender
Male
HSC
2020
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....
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top