 Hello and welcome to the session. Let us discuss the following question. Question says, choose the correct answer. Integral sine square x minus cos square x dx upon sine square x multiplied by cos square x is equal to tan x plus cot x plus c, b tan x plus cos x plus c, c minus tan x plus cot x plus c, d tan x plus sec x plus c. We have to choose correct answer from a, b, c and d. Let us now start with the solution. We have to find integral sine square x minus cos square x dx upon sine square x multiplied by cos square x. Now this integral can be further written as integral of sine square x dx upon sine square x multiplied by cos square x minus integral of cos square x dx upon sine square x multiplied by cos square x. Now this sine square x will get cancelled by this sine square x and this cos square x will get cancelled by this cos square x and we are left with integral of dx upon cos square x minus integral of dx upon sine square x. Now we know 1 upon cos x is equal to sec x. So 1 upon cos square x can be written as sec square x. So here we can write integral of sec square x dx minus we know 1 upon sine x is equal to cos x. So 1 upon sine square x is equal to cos x square x. So here we can write integral of cos x square x dx. Now we know integral of sec square x dx is equal to tan x and integral of cos x square x dx is equal to minus cot x plus c where c is the constant of integration. Now this expression can be further written as tan x plus cot x plus c. So we get integral of sine square x minus cos square x dx upon sine square x multiplied by cos square x is equal to tan x plus cot x plus c. So the correct answer is a. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.