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:
[tex]\frac{sin(x)cos(y)-cos(x)sin(y)}{cos(x)cos(y)}[/tex]
[tex]=\frac{sin(x)}{cos(x)}-\frac{sin(y)}{cos(y)}[/tex]
[tex]=tan(x)-tan(y)[/tex]
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.
