 Hi and welcome to the session. Today we will learn about trigonometric ratios of complementary angles. In right angle to triangle ABC for angle A we have already learned the trigonometric ratios. Now we call that two angles are said to be complementary if their sum is equal to 90 degrees. So in triangle ABC angle B is equal to 90 degrees that means sum of angle A and angle C is equal to 90 degrees which implies angle A and C are complementary angles. So now let us learn the trigonometric ratios for angle C which is equal to 90 degrees minus A. So let us start, sin 90 degrees minus A is equal to cos A also cos 90 degrees minus A is equal to sin A. Next tan 90 degrees minus A is equal to cot A and cot 90 degrees minus A is equal to tan A. Now secant 90 degrees minus A is equal to cosecant A cosecant 90 degrees minus A is equal to secant A. These ratios are true for all values of angle A line between 0 degrees and 90 degrees. Let us try this small example for this. Here we need to evaluate cos 53 degrees upon sin 37 degrees minus tan 68 degrees upon cot 22 degrees. Now to solve this we will use these trigonometric ratios of complementary angles. Now here cos 53 can be written as cos 90 degrees minus 37 degrees upon sin 37 degrees minus. Now 68 is equal to 90 minus 22 so this will be tan 90 degrees minus 22 degrees upon cot 22 degrees. Now we know that cos 90 degrees minus A is equal to sin A so this will be sin 37 degrees upon sin 37 degrees minus. Now tan 90 degrees minus A is equal to cot A so this will be cot 22 degrees upon cot 22 degrees. So this will be equal to 1 minus 1 that is 0. So this is how we can use the trigonometric ratios of complementary angles to simplify our questions. Now let's move on to trigonometric identities. We have three identities. First is sin square A plus cos square A is equal to 1 for 0 degrees less than equal to A less than equal to 90 degrees. Now second is 1 plus tan square A is equal to sin square A for 0 degrees less than equal to A less than 90 degrees. And third is 1 plus cot square A is equal to cos square A for 0 degrees less than A less than equal to 90 degrees. So these are the three identities. Now let's see how we can use them in our questions. Suppose we need to show that cos square A minus 1 into tan square A is equal to 1. So we will start with LHS which is equal to cos square A minus 1 into tan square A. Now we know that cos square A is equal to 1 plus cot square A. So we will replace cos square A over here by 1 plus cot square A. So this will be equal to 1 plus cot square A minus 1 as it is into tan square A. Now here plus 1 and minus 1 will get cancelled and we are left with cot square A into tan square A. Now we know that cot square A is 1 upon tan square A into tan square A as it is. So tan square A will get cancelled from the numerator and denominator and we get 1 which is equal to RHS of the given equation. So using these identities we can prove our questions. So in this session we have learnt trigonometric ratios of complementary angles and trigonometric identities. With this we have finished this session. Hope you must have understood all the concepts. Goodbye and have a nice day.