 Hi and welcome to the session. I am Neha and I am going to help you with the following question. The question says, state whether the following are true or false. Justify your answer. So first of all let's see the first part. It says sin a plus b is equal to sin a plus sin b. So let's find out whether this statement is true or false by taking the value of a equal to 45 degrees and the value of b also equal to 45 degrees. Now first of all let's take the LHS of this statement which is equal to sin a plus b. So substituting the values of a and b we will get sin 45 degrees plus 45 degrees that will be equal to sin 90 degrees and we know that sin 90 degrees is equal to 1. Now let's take RHS. Here RHS is sin a plus sin b. So substituting the values of a and b we will get sin 45 degrees plus sin 45 degrees. Now sin 45 degrees is 1 upon root 2 so this will be plus 1 upon root 2 which is equal to 2 upon root 2 that will again be equal to root 2. So here we can see that LHS is not equal to RHS as LHS is equal to 1 and RHS is equal to root 2. So that means the given statement sin a plus b is equal to sin a plus sin b is false. Now let's see the second part. It says the value of sin theta increases as theta increases. So here let us write the values of sin theta when theta is 0 degrees. So sin 0 is 0 for 30 degrees sin 30 degrees is 1 upon 2 sin 45 degrees is 1 upon root 2 sin 60 degrees is root 3 by 2 and sin 90 degrees is 1. So here theta is increasing from 0 to 90 degrees also sin theta is increasing from 0 to 1. So that means the value of sin theta increases with the value of theta thus our statement is true. Next statement says the value of cos theta increases as theta increases. So now here let us write the values of cos theta now cos 0 is 1 cos 30 is root 3 by 2 cos 45 degrees is 1 upon root 2 cos 60 degrees is 1 by 2 and cos 90 is 0. So here as we can see that as theta increases the value of cos theta decreases from 1 to 0. That means the given statement is false. Fourth statement given to us is sin theta is equal to cos theta for all values of theta. Let's see this table which we made for the last two statements. Here for theta equal to 0 sin theta is 0 and cos theta is 1. So that means for 0 degrees sin theta is not equal to cos theta for 30 degrees again sin theta is not equal to cos theta. So when we observe all the values at different values of theta we can see that sin theta is equal to cos theta only at the value of theta equal to 45 degrees. That is 1 by root 2 for all other values sin theta is not equal to cos theta. So this statement that sin theta is equal to cos theta for all values of theta is not correct. That means it is false. Now the last statement is cot a is not defined for a equal to 0 degrees. Now we already know that tan 0 degrees is equal to 0 and cot 0 degrees will be equal to 1 upon tan 0 degrees. So that will be equal to 1 upon 0 which is not defined. So that means cot a when a is equal to 0 is not defined. So our statement is true. So with this we finished this question and the session as well. I hope you must have enjoyed it. Goodbye, take care and have a nice day.