trigonometry

[crisp crane]

Period of cos(|sinx|-|cosx|)

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[frosty garden]

Hmm what u think the inner function role would be

I might give u hint , like assume a value of x and figure on wut other value of x , u get same value

[crisp crane]

The inner function period is π

[frosty garden]

hmm ye

Now since u know inner function is pie , try and check by putting value of x as pie/2-x , to check if it's time period is pie/2 too

[crisp crane]

Cos(π/2-x) = sin(x)?😢

[frosty garden]

Ye sin x

Not sin (pie/2)

[crisp crane]

Yess

[frosty garden]

Now u remember what type of function is cos?? , like what would happen if we put cos(-x)

[crisp crane]

Cos(π/2+x)=sinx

[frosty garden]

Ye we only need (pie/2-x) for now tho

[frosty garden]

Anyways answer this

[crisp crane]

Same thing

It is even

[frosty garden]

True

So |sinx|-|cosx| or |cosx|-|sinx| , it would be same thing in cos

[crisp crane]

Yes

[frosty garden]

That's why even if u put x-> π/2-x , the function still remains same

[crisp crane]

Where

It is sinx no?

[frosty garden]

Cosx changes in sin x and sinx changes in cosx

[frosty garden]

Here

The function inside

[crisp crane]

I see

I see

[frosty garden]

Ye since f(x) = f(π/2+x) , it's time period is π/2

[crisp crane]

True

Next question

[frosty garden]

We generally recheck again by putting π/4 but in this case it's not necessary

[frosty garden]

Hmm sure

[crisp crane]

I changed it like

tan(arctan3/5- arctan-3/5)

[frosty garden]

It's cos-1(-4/5)
So I think it should tan(-3/5)

[crisp crane]

I see

[frosty garden]

So tan[ 2×arctan(3/5)]

U can solve further i believe

[crisp crane]

How you got this?

Ohh got it

[frosty garden]

Ye u just bring -ve outside

[crisp crane]

So 2×3/5 ?

6/5

[frosty garden]

No

U can't solve tan function when there 2 in multiple

U gotta somehow convert that 2 in whole arc tan function

[crisp crane]

I see

[frosty garden]

I am pretty sure u would have learned 2arctan(x) formula

It's just arctan [2x/(1-x²)]

[crisp crane]

Let me remember it

[frosty garden]

Hmm sure take ur time

[crisp crane]

24/7

[frosty garden]

Hmm nice

U did it

[crisp crane]

arccos(-4/5) not equal to arc cos(4/5)

[frosty garden]

That's true

U would have to write it as
π - arccos(4/5)

[crisp crane]

I see

Arccos(-4/5)+arccos(4/5)=π

[frosty garden]

Yea that was true

[crisp crane]

Is this correct?

[frosty garden]

Yup it's all correct

[crisp crane]

When do we add +π or -π here?

[frosty garden]

Hmn where

[crisp crane]

Arc tanx+arc tanx

[frosty garden]

Ohh so there are some cases for those uk

Like if x>0 or x<0 or less than 1

[crisp crane]

I am confused in those cases

[frosty garden]

Hmm understandable

Hmm lemme see if I can write it down for u

Just gimme some time

Here u go , read it then ask me if u have doubt

Bru my net suck

[timber ginkgo]

Can you explain the last case

If there is negative up and down they will cancel each other

Then why you put π in LHS

[frosty garden]

Yes , but in LHS. ,u see x and y are negatives , so that whole side is negative

So we add pie there

[timber ginkgo]

Ah I see thanks

[crisp crane]

But we add -π

Also

This case missing

[frosty garden]

Well don't always trust Wolfram

Try putting x = 0 , and x= π/2 , u get same value

[frosty garden]

Well ig ur talking about the case 3 only: people generally directly add -π in RHS. ,but to explain it i add it π in LHS

[crisp crane]

Ohh i see got it

[crisp crane]

+close