 Hello and welcome to this session. Let us understand the following problem today. Write the following function in the simplest form. We have tan inverse of cos x minus sin x by cos x plus sin x where x is resonant pi. Now let us write the solution. We have tan inverse of cos x minus sin x by cos x plus sin x. Now dividing numerator and denominator both by cos x. So we get which is equal to tan inverse of cos x by cos x minus sin x by cos x whole divided by cos x by cos x plus sin x by cos x which is equal to tan inverse of 1 minus tan x by 1 plus tan x which is equal to tan inverse of tan pi by 4 minus tan x by 1 plus tan pi by 4 into tan x because tan pi by 4 is equal to 1 which is equal to tan inverse of tan pi by 4 minus x. Using the identity pi by 4 minus x is equal to tan pi by 4 minus tan x whole divided by 1 plus tan pi by 4 into tan x it is equal to pi by 4 minus x. Thus the required answer is pi by 4 minus x. I hope you understood the problem by and have a nice day.