Question

Which expression below can be obtained from 4sin4t by using a power reducing formula?

Select the correct answer below:

1+2cos(4t)
32−2cos(2t)+12cos(4t)
32+2cos(2t)+12cos(4t)
3−2cos(2t)+2cos(4t)

Answer 1

Explanation:

4×sin(4t) = 4×sin(2t + 2t) =

= 4×(sin(2t)cos(2t) + cos(2t)sin(2t)) =

= 4×2×sin(2t)cos(2t) = 8×sin(2t)cos(2t)

but that did not lead anywhere near to any of the answer options.

so, i guess, you made typos in the description and in the answer options.

did you mean maybe

4×sin⁴(t) ?

sin⁴(t) = (3 - 4×cos(2t) + cos(4t))/8

4×sin⁴(t) = 4×(3 - 4×cos(2t) + cos(4t))/8 =

= (3 - 4×cos(2t) + cos(4t))/2 =

= 3/2 - 2×cos(2t) + 1/2 × cos(4t)

is that the real answer option 2 ?

then that is the correct answer.