trigonometry: (A2) Compound angles question

Hi,

Could someone help me out with what this questions asking me exactly?

Thanks

It is asking you to find the value of $\alpha$ such that $\dfrac{1+\tan x}{1-\tan x} \equiv \tan(x+\alpha)$

oH! thankyou

so i’m assuming x and $\alpha$ are two different variables?

sorry if i’m a bit slow we just went over this today ergh

x is the variable.

Alpha is a constant value.

so is the answer 45 because x and alpha must be the same so that alphas eliminated on the RHS?

or am i just lost :’)

Hi,

Could someone help me out with what this questions asking me exactly?


Thanks

Starting with: tan(x + a) = (tan a + tan x) / (1 - tan a tan x)
Notice that if tan a = 1, then the expression becomes identical to what is in the question: (1 + tan x) / (1 - tan x)
So let a = arctan(1) = pi/4 to get tan(x + pi/4).

Hope this helps