Integration

[heady trench]

integrand can be reduced -(cos2x + cosx)

use sum to product in numerator \
$\cos A + \cos B = 2 \cos(\frac{A+B}{2}) \cos(\frac{A-B}{2})$

[remote ferry]

mercy

[heady trench]

then triple angle on cos9x/2

find a wau to cancel numerator and denominator

[rough rose]

Wait

[rough rose]

What does this mean

How i triple angle

Why i triple angle

After this?

Should I expand cos3x

It won't help though

I would just get two cos terms

[heady trench]

,, \cos 3\theta = 4\cos^{3}\theta - 3\cos\theta

[remote ferry]

mercy

[rough rose]

Yeah but how does it help

[heady trench]

apply this to cos9x/2

[heady trench]

,rccw

[heady trench]

take cos3x/2 common

[heady trench]

take 2 common apply 2cos^2t -1 = cos2t inside bracket

[rough rose]

You mean 2cos^t-1=cos2t

[heady trench]

,,2cos^2(\theta) -1 = cos(2\theta)

[remote ferry]

mercy

[rough rose]

I apply this on 4cos^2(3x/2)?

[heady trench]

yes on 4cos^2(3x/2)-3

[rough rose]

How

It is not in that form

[heady trench]

,, 4cos^2(\frac{3x}{2})-3 = 4cos^2(\frac{3x}{2})-2-1 = 2(2cos^2(\frac{3x}{2})-1) -1

[remote ferry]

mercy

[rough rose]

Ohhhhh

Damn

[heady trench]

dont forget cosx/2

[heady trench]

^

[rough rose]

It came in uv form

Multiplication form

I can use 2cosa cosb formula

,,2cosacosb

[remote ferry]

SPYLEX

[rough rose]

What

Ayo bro its done i guess

[heady trench]

yes

[rough rose]

This came in my exam i couldn't do it

I dont think if anything like this come i can do it

I dont know how to think like this in exam

[heady trench]

yes the manipulation was wierd i do not know if there is an easier way but if you see double angle type shit then it may be reducable

[rough rose]

What does double angle mean

[heady trench]

,, 2\theta

[remote ferry]

mercy

[rough rose]

Yeah i tried to break cos3x in denominator it made it worse

And for this question my whole paper went shit

This question was so frustrating