show that: [tan(x+p/4).tan(x-p/4)]=1

Question

Show that:

[tan(x+π/4).tan(x-π/4)]=1

 

please show workings.

 

I ended up at.

1.tan(x)+1/1+tan(x)=1

not sure i'm right though.

Answer 1

Use trigonometric identities.

 

 

Hint:  Use the double formula for tangent:

 

tan(x+y) = [tan(x) + tan(y)]/[1-tan(x)tan(y)] 

 

                                    and

 

tan(x-y) = [tan(x) - tan(y)]/[1+tan(x)tan(y)]