why isn't tan θ cancelled out in this fraction?

[bushra1175]

Hi everyone. The right side of this equation is being simplified below but I don't understand why tan θ isn't cancelled out like tan 135 is? I don't know how they got the end result

 

[Steven G]

tan 135 is not being cancelled out. Rather it is being replaced with its exact value. If 1 - tan135*tanθ becomes 1 + tanθ then what do you think tan135 must equal?

 

[bushra1175]

tan 135 is not being cancelled out. Rather it is being replaced with its exact value. If 1 - tan135*tanθ becomes 1 + tanθ then what do you think tan135 must equal?

That's what I'm struggling to understand actually. I don't get how became , and became

 

[Steven G]

If tan 135 = -1, then 1 - tan135*tanx = 1 - (-1)tanx = 1+tanx
tan135 + tanx = -1 + tanx.
Is it not clear that tan135 is being replaced with -1?

Also you should know that tan135 is some real number and for it to disappear from the equation then maybe it was replaces with its actually value.

You need to see that on your own.

 

[Steven G]

If x + tanθ = -1 + tanθ you should be able to solve for x. Just subtract tanθ from both sides and get x=-1

Similarly if you have If tan135 + tanθ = -1 + tanθ you should be able to solve for tan135. Just subtract tanθ from both sides and get tan135=-1

 

[bushra1175]

If tan 135 = -1, then 1 - tan135*tanx = 1 - (-1)tanx = 1+tanx
tan135 + tanx = -1 + tanx.
Is it not clear that tan135 is being replaced with -1?

Also you should know that tan135 is some real number and for it to disappear from the equation then maybe it was replaces with its actually value.

You need to see that on your own.

oh! sorry I've been so focused on rearranging the components that I didn't realise tan 135 is actually a value you can get in a calculator. My apologies.