tan(pi/4 - theta) %2B tan(pi/4 %2B theta)=2*sec(2*theta)

1.	tan(pi/4 - theta) %2B tan(pi/4 %2B theta)=2sec(2theta)
Answer» Let theta = x LHS: tan(pi/4 + x) + tan(pi/4 - x) =(1+tan x)/(1-tan x)+ (1- tan x)/(1+tan x) =[(1+tan x)^2 +(1-tan x)^2]/[(1-tan^2 x] =2(1+tan^2 x)/(1-tan^2 x) =2(cos^2 x+sin^2 x)/(cos^2x-sin^2 x) =2/cos2x = 2sec2x= RHS Hence proved

tan(pi/4 - theta) %2B tan(pi/4 %2B theta)=2sec(2theta)

Answer»

Let theta = x

LHS: tan(pi/4 + x) + tan(pi/4 - x) =(1+tan x)/(1-tan x)+ (1- tan x)/(1+tan x) =[(1+tan x)^2 +(1-tan x)^2]/[(1-tan^2 x] =2(1+tan^2 x)/(1-tan^2 x) =2(cos^2 x+sin^2 x)/(cos^2x-sin^2 x) =2/cos2x = 2sec2x= RHS

Hence proved

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tan(pi/4 - theta) %2B tan(pi/4 %2B theta)=2*sec(2*theta)

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tan(pi/4 - theta) %2B tan(pi/4 %2B theta)=2sec(2theta)