Question

i want to write this trig expression using power reducing identities : 6cos²x...what do I do with the 6?

Answer 1

i can use the identity \[\frac{ 1+\cos2x }{ 2 }\]

Answer 2

but i dont know how to deal with the 6...

Answer 3

\[\cos2x = 2\cos^2x - 1\]

Multiply both sides by 3

\[3\cos2x = 6 \cos^2 x - 3\]

Answer 4

\[6\cos^2x = 3 \cos2x + 3\]

Answer 5

ah okay!!

Answer 6

@lsugano Just plug whatever you wrote above to replace cos²x, then simplify

Answer 7

Wait then what if the exponent changed to like for example...4?

Answer 8

like cos⁴x??

Answer 9

Don't jump ahead when you don't even have the base yet!

Answer 10

oh..okay

Answer 11

Are you fine with this question?

Answer 12

yes! i got that! i actually ran into the exact same question cos⁴x

Answer 13

= (cos²x)²
= ....

Answer 14

cosx^4

Answer 15

oh so its \[\frac{ (1+\cos2a)^2 }{ 2^2 }\]

Answer 16

Yup, now expand the square :)

Answer 17

\[\frac{ 1+2\cos2a+\cos^2a }{ 4 }\]

Answer 18

The third term is cos ² (2a)

Answer 19

ohh yess silly mistake ><

Answer 20

i should bring the 4 up?

Answer 21

how do i simplify than this?

Answer 22

Again double the angle to reduce power!

Answer 23

double?? why ?