Trigonometry to

[VeeN22]

Please help me.
I was working out a few problems and came about this confusing one.
Cos^2x + 2Cosx Sinx - 8 sin^2x = 0

I simplified a little bit, eventually getting
1- Sin^2x + 2Cosx Sinx - 8 Sin^2x = 0

Which equation do I use because both:
(a+b)^2 = a^2 + b^2 - 2ab
and
(a - b)^2 = a^2 - 2ab + b^2 are not giving me the desired outcome.

 

[MarkFL]

I would factor as:

[MATH](\cos(x)+4\sin(x))(\cos(x)-2\sin(x))=0[/MATH]

 

[VeeN22]

=Cos^2x - 2SinCosx + 4 SinxCosx - 8 Sin^2x
=Cos^2x + 2SinxCosx - 8 Sin^2x
=Sin 2x + Cos 2x - 7 Sin^2x

= 1-Cos^2x + 1-Sin^2x - 7Sin^2x
=1-Cos^2x - 6Sin^2x
=Sin^2x - 6Sin^2x
= - 5Sin^2x

Lol this looks weird?@MarkFL

 

[MarkFL]

It appears you are confusing:

[MATH]f^2(x)[/MATH] with [MATH]f(2x)[/MATH]
where \(f\) is the sine and cosine functions.

 

[topsquark]

@VeeN22
In relation to MarkFL's comment it would be helpful for you in the future to use parenthesis around the argument. For example, cos^2(x) or cos(2x). It helps organize your work better.

-Dan

 

[VeeN22]

It appears you are confusing:

[MATH]f^2(x)[/MATH] with [MATH]f(2x)[/MATH]
where \(f\) is the sine and cosine functions.

Okay thanks

 

[VeeN22]

@VeeN22
In relation to MarkFL's comment it would be helpful for you in the future to use parenthesis around the argument. For example, cos^2(x) or cos(2x). It helps organize your work better.

-Dan

You're right.