Question

Which of the following are identities?

Check all that apply.
A. 1- tan² x / 2 tan x = 1 / tan 2x
B. (Sin x – cos x)² = 1 + sin 2x
C. Sin 8x = 2 sin 4 x cos 4x
D. Sin x + sin 5x / cos x + cos 5x = tan 3x

Answer 1

Among the given options, the identities are A and B.

Step-by-step explanation:

There are two identities among the given options. These are:

A. 1- tan² x / 2 tan x = 1 / tan 2x
B. (Sin x – cos x)² = 1 + sin 2x

Let's check them:

1. For A, we can use the trigonometric identity tan² x + 1 = sec² x to rewrite the left-hand side of the equation. After some simplification, we end up with 1 = 1, which is always true. Therefore, A is an identity.
2. For B, we expand the left-hand side using the formula (a - b)² = a² - 2ab + b². After some simplification, we find that the left-hand side is equal to the right-hand side, which means B is an identity.

Therefore, the identities among the given options are A and B.