Question

Verify the identity
sin4(t)=4sin(t)cos^3(t)-4sin^3(t)cos(t)

Answer 1

@dumbcow

Answer 2

can i show you my work?

Answer 3

is that sin^4(t) or sin(4t) ?

Answer 4

it's sin(4t)

Answer 5

\[ \sin (4t)=4\sin(t)\cos^3(t)-4\sin^3(t)\cos(t)\]

Answer 6

do you see my work okay?

Answer 7

yes but its for cos^4(t) ?

Answer 8

oh no i'm sorry i asked the wrong question

Answer 9

one moment please

Answer 10

use the power reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Answer 11

10cos^4x

Answer 12

can you help me with that?

Answer 13

ok 1 error in your work is:
\[\cos^2 (2x) = \frac{1 + \cos(4x)}{2}\]

Answer 14

wait which step ? can you circle it in my work?

Answer 15

at this step:
\[\cos^4 x = \frac{1 + 2 \cos (2x)+ \cos^2 (2x)}{4}\]
where you substituted for cos^2(2x)

Answer 16

i circled something in the picture

Answer 17

yes where you circled is the error

Answer 18

what did i do wrong? distrubution?

Answer 19

im not sure what you did, but the correct substitution is
\[\cos^2 (2x) = \frac{1 + \cos(4x)}{2}\]

Answer 20

i was trying to get the numerator to have the same denomiator so i did 2/2and distrubted that

Answer 21

2/2 is just 1 ?

common denominator after substitution is 8

Answer 22

this may help

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Power-reduction_formula

Answer 23

\[\cos^4(x) = \frac{1+2\cos(2x) + \frac{1+\cos(4x)}{2}}{4} = \frac{2 + 4\cos(2x) + 1+\cos(4x)}{8}\]

Answer 24

helllo?