 Hello and welcome to the session. I am Arsha and I am going to help you with the following problem which says proves that tan pi upon 4 plus x upon tan pi upon 4 minus x is equal to 1 plus tan x upon 1 minus tan x whole square. Let us now begin with the solution and here we will solve the left hand side and show that it is equal to the right hand side. Now left hand side is tan pi upon 4 plus x upon tan pi upon 4 minus x. Now the formula of tan A plus B is tan A plus tan B upon 1 minus tan A into tan B. So here in place of B we have pi upon 4 and in place of B we have x. So it can be written as tan pi upon 4 plus tan x upon 1 minus tan A that is pi upon 4 into tan B which is tan x upon. Now we will apply the formula of tan pi by 4 minus x. So the formula of tan A minus B is equal to tan A minus tan B upon 1 plus tan A into tan B. So writing tan pi by 4 minus x by using this formula it can be written as tan pi upon 4 minus tan x upon 1 plus tan pi upon 4 into tan x. So by using these two formulas we have expanded the left hand side and now let us write it further. Now tan pi upon 4 is 1 plus tan x upon again tan pi by 4 is 1 so we have 1 minus 1 into tan x is tan x upon similarly 1 minus tan x upon 1 plus tan x which can be written as 1 plus tan x upon 1 minus tan x into 1 plus tan x upon 1 minus tan x which is further equal to 1 plus tan x whole square upon 1 minus tan x whole square which is further equal to 1 plus tan x upon 1 minus tan x whole square and which is the right hand side that we have to prove. Thus pi upon 4 plus x upon tan pi upon 4 minus x is equal to 1 plus tan x upon 1 minus tan x whole square. So this proves the version hope you enjoyed it take care good day.