Question

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos^3 x

Answer 1

I think the answer is D, is that correct?

Answer 2

pi/3

Answer 3

sorry, there are choices?

Answer 4

Yes

Answer 5

pi/3 is not a choice

Answer 6

and it's cos cubed not cos 3x...

Answer 7

Fixed, sorry about that.

Answer 8

no worries...
if it's pi or 0 then the sine term disappears but cos = cos cubed for those values, right?
and it can't be pi/2 because the cos factors on the left meaning the left side is 0, same as the right side, correct?
so which remains?

Answer 9

Just pi, so A.

Answer 10

no... sin (pi) = 0 => cos pi - 0 = -1 = (-1)^3 = cos^3 pi

Answer 11

Well in that case it'd be pi/4

Answer 12

\[\frac{ 1 }{ \sqrt{2} }-\frac{ 1 }{ \sqrt{2} }\frac{ 1 }{ \sqrt{2} }=\frac{ \sqrt{2}-1 }{ 2 }\neq \left( \frac{ 1 }{ \sqrt{2} } \right)^{3}=\frac{ 1 }{ 2\sqrt{2} }= \frac{ \sqrt{2} }{ 4 }\]

Answer 13

dude... cos (pi/4) = sin (pi/4) = 1/sqrt(2)

Answer 14

Oh

Answer 15

Thanks

Answer 16

you're welcome

Answer 17

gotta know your trig...