quick question (trig equations)

[zealous echo]

What do we need to find here?

[quasi hornet]

solving for x

the answers show that you need to subtract sin from both sides and factor it out

then solve for sinx = 0 and cosx = 1/2

but i want to know why im not able to divide by sinx

because that i what i would have initially done and it wouldve been wrong

[zealous echo]

There are two roots possible for the given equation

You can do that way too, but you'll get only one root that way

Yk quadratic equations?@quasi hornet

[quasi hornet]

yea

[zealous echo]

And you gotta find all the roots of the equation, i.e., all the values for x

It's the same here

[quasi hornet]

the x intercepts?

[zealous echo]

Bruh just subtract sinx from both sides or take the right side one to the left and take it common

You'll get two values for x that way

[quasi hornet]

yeah ik

was just curious to know why my initial method wouldnt have worked

[zealous echo]

It'd work but here you can clearly see that there are two values of x, one for sinx and the other one for cosx

Idk if my reasoning is correct either

But you gotta remember the quadratic principle here

[quasi hornet]

i dont see a quadratic in the equation tho

[zealous echo]

You can just assume 0.x^2 or smthng

But here if you can see two values for x you gotta find both of them

As simple as that

[quasi hornet]

right

so i just have to notice that there is a sinx and a cosx

[zealous echo]

Yup

[quasi hornet]

ok thanks

[zealous echo]

Solve tons of them and you'll get an idea on how it works