 Hello friends, so we have seen two relations so far Using trigonometric ratios now in this session. We are going to discuss the third one So before we go to the third one, let's recap what we have learned so far. We have learned so far that one is this sine square theta plus Cos square theta is equal to one irrespective of the value of theta. This is true This is true. This is valid for every value of theta. Hence it is called a trigonometric identity as well Now and secondly, we learned that cosecant square theta is equal to 1 plus cot square Theta. These are the two relations we have learned now. We are going to deal with the third one here Now in the last two cases we divided this equation obtained by Pythagoras theorem By first h square and then p square correct this we have already discussed now what we are going to do is We are going to divide dividing equation 1 equation 1 by B square now, okay So what will we get? We will get h square by b square is equal to p square by b square plus B square by b square, isn't it? This is doable now. This implies h upon b whole square is equal to p upon b whole squared plus 1 right now look at this triangle ABC where This is hypotenuse. This is base and this is perpendicular Now if you see h by b, what is h by b here h upon b is nothing but secant theta secant theta because it is 1 upon cos theta. Now, what about p by b? So if you see p upon b here p, this is p and this is p and this is b. p upon b is nothing but tan theta tan theta right so we can replace or substitute them here So h by b I can write as secant theta whole square is equal to tan theta whole squared plus 1 This is nothing but secant square theta is equal to tan square theta plus 1 this is another very important relationship now again as the other cases we can express this Relation into multiple forms. So I can write secant square theta minus tan square theta Is equal to 1. This is one way of looking at it another way of looking at it is secant square theta minus 1 is equal to tan square theta so this implies this is secant theta minus tan theta times secant theta plus tan theta is equal to 1 because if you see this is a square minus b square form So a square minus b square is a minus b a plus b We know this similarly the same concept if you use here you will get secant theta minus 1 times secant theta plus 1 is equal to tan square theta so keep these forms also in mind these are very very useful Way of expressing the same relation into multiple ways now these things are going to be very very useful while Proving trinometric identities. So keep these relations in very much in your mind. Okay