 Hi, this is Meenu and helping you to solve the following problem. It says, prove the following. We have to prove that tan 4x is equal to 4 tan x into 1 minus tan square x upon 1 minus 6 tan square x plus 10 to the power 4x. So let us first understand the formula which we will be using to solve the problem. It is tan 2y is equal to 2 tan y upon 1 minus tan square y. So this is the key idea to solve the following problem. Let us now proceed on to the solution and we first find out LHS which is tan 4x. Now tan 4x can be written as tan 2 into 2x. Now we apply the formula of tan 2x to this. So we get 2 tan 2x because here y is 2x upon 1 minus tan square 2x. Now again we can see that we can apply the formula of tan 2x here. So we again apply the formula so that it becomes 2 into 2 tan x upon 1 minus tan square x upon 1 minus 2 tan x upon 1 minus tan square x whole because we have a square. Now let us simplify 2 into 2 tan x is 4 tan x upon 1 minus tan square x upon taking the LCM. LCM would be 1 minus tan square x whole square. So we get here 1 minus tan square whole square minus 2 tan x whole square upon 1 minus tan square whole square. Again this is equal to 4 tan x upon 1 minus tan square x into taking the reciprocal of this 1 minus tan square x whole square upon 1 minus tan square x whole square minus 2 tan x whole square. Now we can see that 1 minus tan square x gets cancelled with 1 of the 1 minus tan square x because there is part 2. So we are left with 4 tan x into 1 minus tan square x upon 1 minus tan square x whole square minus 2 tan x whole square. Now again this is equal to 4 tan x into 1 minus tan square x upon. Opening the formula for a minus b whole square we get 1 plus 10 to the power 4 x minus 2 tan square x minus 4 tan square x 2 tan square whole tan x whole square is 4 tan square x and now this is equal to 4 tan x into 1 minus tan square x upon 1 minus 6 tan square x plus 10 to the power 4 x and which is our RHS. This is what we had to prove. Hence the result is proved. So this completes the question. Bye for now. Take care. Hope you enjoyed this session.