Which of the following are identities? check all that apply. a) sin3x/sinx cosx =4cosx -secx b) sin6x= 2sin3x cos3x c) sin3x-sinx/cosx+cosx= tanx d) (sinx+cosx)^2=1+sin2x

  option b and d are identities.

step-by-step explanation:

in case a:

we have

using

hence, option a is incorrect we will not get right hand side equal to left hand side.

in case b:

using

here, we will split as

hence, option b is correct.

in case c:

we have

hence, option c is incorrect.

in case d:

we have

we will open the left hand side of the given equation by using

we know that and

hence, we will finally get

hence, option d is correct.

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4