 Hello friends, so welcome to another session on trigonometry in this session. We are going to deal with some T ratios for some specific angles Okay, and we have already seen the various values of T ratios for theta equals to 0 and theta equals to 19 previous sessions in This session we are going to discuss what will be the different T ratios for theta is equal to 45 degrees. What does it mean? It means that if there is a triangle ABC and angle A is 90 degrees such that angle C is 45 and Hence by angles some property angle B also is 45 degrees Then what will be the values of different T ratios that is sine 45 cos 45 and all that now, let us say in triangle ABC AC Side AC is equal to AB is equal to A Both sides are equal. Why because since the two angles are equal to 45 degree here. This is 45 and this is also 45 So ABC is an isosceles triangle ABC Triangle ABC is an isosceles triangle Correct because of this what will happen the angles or sorry the sides opposite of the equal angles will also be equal and Hence if AC is a AB will also be a now since angle B AC is 90 degrees That means we can apply Pythagoras theorem. So hence BC square is Equal to a square plus a square, right? So BC is equal to nothing but under root 2 a square Which is nothing but a times root 2 right since there is a square on a so I can Pull it out of the square root sign. So it is a root 2 now. Let us now go for the different T ratios So hence sign of 45 degrees What is sign of any angle is nothing but opposite divided by hypotenuse so opposite is a clearly and Whichever angle you take whether you take C or B opposite is a and the hypotenuse is the root 2 times a So hence sign 45 will be simply 1 by Root 2 now it doesn't depend on the sides of the triangle Correct any ways the T ratios never never depend on the side length of the triangle there since they are ratios now Costs of 45 if you can notice Costs of 45 again will be adjacent by Hypotenuse so a upon root 2 a again. So it is again 1 upon root 2 isn't it now tan of 45 degrees is nothing but sign 45 degrees upon Costs 45 either you can take this route and say it is nothing but a upon a a by root 2 Sorry, I'm sorry. It is not it is not a by root 2. It is 1 upon root 2 So it is 1 upon root 2 divided by 1 upon root 2, which is nothing but one or you can always say That tan is perpendicular by base so a by a is good one now what is cosecant 45 degrees So cosecant 45 degrees 1 upon sign 1 upon sign 45 degrees Hence it is nothing but 1 upon 1 by root 2 hence it is Root 2 Similarly secant upon secant 45. Sorry Now here I have mentioned an extra theta, right? So hence secant 45 degrees is Nothing but 1 upon cost 45 degrees is again root 2 correct and cot 45 is 1 upon tan 45 Or base by perpendicular whichever way you want to write is 1 right so always remember sign of 45 is 1 by root 2 cost of 45 degrees is 1 by root 2 Then of 45 is one cosecant 45 is root 2 secant 45 is root 2 and cot 45 is 1 you must remember these values because they are going to be used multiple number of times in various problems solving Thank you