 Hi and welcome to the session. I'm Priyanka and let us discuss the following question. It says find sin x by 2 cos x by 2 and tan x by 2 when the value of cos x is given to us as minus 1 by 3 and also x is in quadrant third Let us start with our solution. The value of cos x is equal to minus 1 by 3 So we can easily find the value of sin x by 2 as we know that it formula is 1 minus cos x by 2 on Substituting its value we have 1 minus minus 1 by 3 divided by 2 which gives us and further calculation gives us 4 by 6 2 by 3 and hence the answer comes out to be root 2 by root 3 on rationalizing the denominator We have the answer as root 6 by 3 and hence we can write That our answer that is the value of sin x by 2 comes out to be after rationalizing the denominator That is root 6 by 3 Proceeding on further to find out the value of cos x by 2 here also will substitute the value of cos x in the formula and we can easily reach to our required answer Proceeding on and we have the value as after LCM. It will be 3 minus 1 divided by 2 which gives us the value of 1 by root 3 which on rationalizing gives us the value as root 3 by 3 since it's given that the x lies in the third quadrant hence its value will be negative Proceeding on further to find out the value of tan x by 2 it will be sin x by 2 divided by cos x by 2 and it will be root 6 by 3 divided by minus root 3 by 3 Which on simplification will give us the value as minus root 2 So this completes the question that was required to be found out I hope you enjoyed the session and remember the formula for sin x by 2 cos x by 2 and tan x by 2. Bye for now