Question

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)

Answer 1

Answer:

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:

$\frac{sin(x)cos(y)-cos(x)sin(y)}{cos(x)cos(y)}$

$=\frac{sin(x)}{cos(x)}-\frac{sin(y)}{cos(y)}$

$=tan(x)-tan(y)$

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.