# inverse trig compound angle (1 Viewer)

#### yolo tengo

##### Active Member

how do i do this question? i know i’m supposed to use the compound angle formula but like how…

question b btw^

#### ExtremelyBoredUser

##### Bored Uni Student
View attachment 38510

how do i do this question? i know i’m supposed to use the compound angle formula but like how…
Let me give you hints so you get this question by yourself. Note I skimmed over the Q, this isn't a sol but moreso a method of trying find sols by yourself.

Here's a very standard way most students will do;

I think applying tan() to both sides will help

Among with the identity tan(A-B) = ??? (You should know that), your goal is to find what A and B must be (should be obvious).

After you did that, rest should be self explanatory.

Once you did that, try reverse engineering and see how A) fits in. This is the method I used when I was stuck in questions, I would do it the brute force way then try to find a more easier way.

Try to avoid reading solutions, just find it yourself since these are quite elementary questions and the last thing you want is to be memorising qs like this.

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#### ExtremelyBoredUser

##### Bored Uni Student
I encourage @synthesisFR @Pethmin or anyone else to post a solution here, I think a good way of improving in maths esp. in this forum is just trying to explain how things work.

Though I'd highly encourage @yolo tengo to retry the question and possibly find a sol by himself.

#### synthesisFR

##### Well-Known Member
I encourage @synthesisFR @Pethmin or anyone else to post a solution here, I think a good way of improving in maths esp. in this forum is just trying to explain how things work.

Though I'd highly encourage @yolo tengo to retry the question and possibly find a sol by himself.
idk how to use latex

#### Average Boreduser

##### Well-Known Member
I encourage @synthesisFR @Pethmin or anyone else to post a solution here, I think a good way of improving in maths esp. in this forum is just trying to explain how things work.

Though I'd highly encourage @yolo tengo to retry the question and possibly find a sol by himself.
Just tried like 9 times (i did this in du like last yr) but I think I've only learnt how to do it with the same trig function not two like the one yolo is stuck on

#### synthesisFR

##### Well-Known Member
ill try explaning it if the answer is 67.5?

#### synthesisFR

##### Well-Known Member
screw it hope u understand this because i like stream of consiousness writing without caring about grammar imma create my own litearrayr movement

so basically its inverse trig question ur trying find angles
so u gonna let a= arccosx and b= arcsinx
from here u get cos alpha= x and sin beta=x so cosalpha is equal to sin beta
so then u draw a triangle and realise that both traingles are the same triangle as they are similar the angle are just opposite
so alpha is on one angle and beta is on the other
from here u get the property that alpha plus beta is equal to 90
also from the given condition alpha minus beta is equal to 45
so u have a simultaneious equation
if u add these two 2 alpha is 135
so alpha is 67.5 and thats cos inverse x

no im not bothered providing a picture bc im lazy

so yeah for invrese trig problems u are involving angles what ive learnt through practice is usually u wanna get rid of negative signs using inverse idenitites if ur trying to prove them, then u let the different trigs equal to angles which u can find conditions usuing and finally if that doesnt work u can also try what @ExtremelyBoredUser said by 'trigging' both sides

#### unofficiallyred12

##### Member
an alternative method of approaching this q rather than the more conventional (for hsc at least) method that has already been mentioned, is to note that arcsinx + arccosx = pi/2, then simply add the two equations together.

#### synthesisFR

##### Well-Known Member
an alternative method of approaching this q rather than the more conventional (for hsc at least) method that has already been mentioned, is to note that arcsinx + arccosx = pi/2, then simply add the two equations together.
yeha im stupid i forgot i could just use that identity idk why i derived it
ig its because i always do that systematic approach
Ps are u allowed to quote that identity? bc its not on the reference sheet

#### yolo tengo

##### Active Member
I encourage @synthesisFR @Pethmin or anyone else to post a solution here, I think a good way of improving in maths esp. in this forum is just trying to explain how things work.

Though I'd highly encourage @yolo tengo to retry the question and possibly find a sol by himself.
thanks bro also i'm a girl

#### Masaken

##### Clown™
Ps are u allowed to quote that identity? bc its not on the reference sheet
yea it's an established identity, just cos it's not on the ref sheet doesn't mean you can't, they omit a few anyway

#### ExtremelyBoredUser

##### Bored Uni Student
yea it's an established identity, just cos it's not on the ref sheet doesn't mean you can't, they omit a few anyway
Yeah, its good to just memorise obscure identities such as these because it comes in handy if you can save time on questions such as these. I see a lot of exam markers do this where they have a conventional question but tweak it in a manner such that students who went the extra mile to learn an identity are rewarded.

I would also try learning about arctan(x) + arctan(1/x) identity and other stuff like that, being familiar with such trig relations will be sooo handy esp. for integration later on.

#### yolo tengo

##### Active Member
Yeah, its good to just memorise obscure identities such as these because it comes in handy if you can save time on questions such as these. I see a lot of exam markers do this where they have a conventional question but tweak it in a manner such that students who went the extra mile to learn an identity are rewarded.

I would also try learning about arctan(x) + arctan(1/x) identity and other stuff like that, being familiar with such trig relations will be sooo handy esp. for integration later on.
ill do this question later, did too many inverse trig questions and my brain got fried

#### synthesisFR

##### Well-Known Member
Yeah, its good to just memorise obscure identities such as these because it comes in handy if you can save time on questions such as these. I see a lot of exam markers do this where they have a conventional question but tweak it in a manner such that students who went the extra mile to learn an identity are rewarded.

I would also try learning about arctan(x) + arctan(1/x) identity and other stuff like that, being familiar with such trig relations will be sooo handy esp. for integration later on.
do u have like a formula list of what ur allowed bc sometimes i feel like i might lose marks
for examples the area of a minor segment i always derive by doing sector - triangle but some ppl just memmorise the formula?

#### ExtremelyBoredUser

##### Bored Uni Student
do u have like a formula list of what ur allowed bc sometimes i feel like i might lose marks
for examples the area of a minor segment i always derive by doing sector - triangle but some ppl just memmorise the formula?
No the HSC reference sheet is good enough. You don't need to memorise obscure formulas, if you do go past them its good to just keep a memory of them just in case.

#### synthesisFR

##### Well-Known Member
No the HSC reference sheet is good enough. You don't need to memorise obscure formulas, if you do go past them its good to just keep a memory of them just in case.
wat abt 4u
like integrating secx can i just state it or do i have to do times the top and bottom by secx + tanx and then rev chain it?

#### ExtremelyBoredUser

##### Bored Uni Student
wat abt 4u
like integrating secx can i just state it or do i have to do times the top and bottom by secx + tanx and then rev chain it?
If you're doing proof I think you got to be thorough else for normal Qs im sure its fine. For secx, im pre sure u can just integrate it normally? I don't think you need to show that step

#### unofficiallyred12

##### Member
I think it depends on mark allocation. If they allocate like 2 marks to proving the integral of secx, quoting it will only give u one mark. But if it's a one mark q, quoting the answer should be fine