Prove that tan(180 - x) = -tan(x)

We have to prove that tan(180-x) = -tan(x)

Solution

We know the identity

tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

Now we will substitute A = 180 and B = x in the above identity we get

tan(180-x) = [(tan 180 – tan x)/(1 + tan 180 tan x)]

We have learnt that tan 180 = 0

so we get the above equation as

tan(180-x) = [(0 – tan x)/(1 + 0 tan x)]

tan(180-x) = -tan(x)

Hence Proved

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