 Hello and welcome to the session. In this session we discussed the following question which says, show that cos square phi minus sine square phi equal to 2 tan phi upon 1 minus tan square phi is not an identity. So we are given this trigonometric equation, we have to show that it is not an identity. Let's see its solution. We know that the trigonometric equation is called a trigonometric identity if it is true for all values of the angle. So if we have to show that a given trigonometric equation is not an identity then we will find a single value of theta which does not satisfy the trigonometric equation. So here our trigonometric equation is cos square phi minus sine square phi is equal to 2 tan phi upon 1 minus tan square phi. So for this we will find a single value of phi which does not satisfy this equation. Let this equation be equation 1. Now we substitute phi equal to 30 degrees in equation 1. Let's see if phi equal to 30 degrees satisfy this equation or not. On substituting phi equal to 30 degrees we would get the LHS as cos square 30 degrees minus sine square 30 degrees. Now cos square 30 degrees is given as root 3 upon 2 whole square since cos 30 degrees root 3 upon 2 minus sine square 30 degrees written as 1 upon 2 whole square since we know that sine 30 degrees is 1 upon 2 so this is further equal to 3 upon 4 minus 1 upon 4 which is equal to 2 upon 4 and from here we get this is equal to 1 upon 2. So we now have LHS is equal to 1 upon 2. Now let's consider the RHS. RHS is 2 tan phi upon 1 minus tan square phi here also we will substitute phi equal to 30 degrees. So we get this is equal to 2 tan 30 degrees upon 1 minus tan square 30 degrees which is further equal to 2 into now tan 30 degrees is 1 upon root 3 1 minus 1 upon root 3 whole square since we know that tan 30 degrees is 1 upon root 3. This further is equal to 2 upon root 3 upon 1 minus 1 upon 3 this gives us 2 upon root 3 upon 2 upon 3 so this is equal to 2 upon root 3 multiplied by 3 upon 2. Now here 2 cancels with 2 and this is equal to root 3. So we get RHS is equal to root 3. So as you can see that NHS is not equal to the RHS that is phi equal to 30 degrees that's not satisfying equation 1 hence we say that equation 1 is not an identity. So we have proved that the given trigonometric equation is not an identity. With this we complete the session hope you understood the solution of this question.