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# Prove the following: tan (π/4 + x) / tan (π/4 - x) = [(1 + tan x) / (1 - tan x)]^{2}

**Solution:**

LHS = tan (π/4 + x) / tan (π/4 - x)

= [(tan π/4 + tan x) / (1 - tan π/4 tan x)] / [(tan π/4 - tan x) / (1 + tan π/4 tan x)]

[because tan (A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B) ]

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

[(by trigonometric table, tan π/4 = 1]

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

= [(1 + tan x) / (1 - tan x)]^{2}

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 7

## Prove the following: tan (π/4 + x) / tan (π/4 - x) = [(1 + tan x) / (1 - tan x)]^{2}

**Summary:**

We got, tan (π/4 + x) / tan (π/4 - x) = [(1 + tan x) / (1 - tan x)]^{2}. Hence Proved

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