 Hello and welcome to the session. The given question says, prove that 1 divided by sec x minus tan x minus 1 divided by cos x is equal to 1 divided by cos x minus 1 divided by sec x plus tan x. Let's start with the solution and here we shall be simplifying the left hand side and the right hand side of this side by side and lastly we shall be showing that the result of both the sides comes equal. So we are given that 1 divided by sec x minus tan x minus 1 divided by cos x. We have to show that it is equal to 1 divided by cos x minus 1 divided by sec x plus tan x. Now we know that 1 divided by cos x is equal to sec x therefore this can further be written as 1 divided by sec x minus tan x minus sec x is equal to sec x minus 1 divided by sec x plus tan x. Now we know that sec square x is equal to 1 plus tan square x so this implies that 1 is equal to sec square x minus tan square x. Now this is of the form a square minus b square and its formula is a minus b into a plus b so we can write 1 as sec x minus tan x into sec x plus tan x. So by using this this can further be written as sec x minus tan x into sec x plus tan x divided by sec x minus tan x minus sec x and this is equal to sec x minus sec x minus tan x into sec x plus tan x divided by sec x plus tan x or before the wrap sec x minus tan x cancelling with sec x minus tan x and here sec x plus tan x with sec x plus tan x. So here we are left with sec x plus tan x minus sec x is equal to sec x minus of sec x minus tan x. So on opening the bracket we have on the right hand side sec x minus sec x plus tan x and on the right hand side as it is now cancelling plus sec x cancels out with minus sec x and here also so we have tan x is equal to tan x. So the left hand side is equal to right hand side on simplifying thus we have 1 divided by sec x minus tan x minus 1 divided by cos x is equal to 1 divided by cos x minus 1 divided by sec x plus tan x. So this completes the session. Bye and take care.