Which of the following are identities? check all that apply. a) tan x - tan y = sin(x-y)/cosxcosy b) 1 - tanxtany = sin(x+y)/sinxsiny c) tan(x-pie/4) = tanx-1 d) cos(x+pie/6) = -sin(x-pie/3)

The correct answer option is a) tan x - tan y = sin(x-y)/cosxcosy.

Step-by-step explanation:

The option a) tan x - tan y = sin(x-y)/cosxcosy is an identity. Let us prove it:

The right side is equal to:

which is equal to the left side.

Hence, tan x - tan y = sin(x-y)/cosxcosy is an identity.

While rest of the options do not equal to each of their sides so they are not identities.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3