Question 1: Find the maximum and minimum values of each of the following trigonometrical expressions:
Answer:
We know
Question 2: Reduce each of the following expressions to the sine and cosine of a single expression:
Answer:
Multiplying and dividing by we get
Also
Multiplying and dividing by we get
Similarly,
Multiplying and dividing by we get
Similarly,
Question 3: Show that is positive
Answer:
which is a positive number as
is in first quadrant.
Question 4: Prove that lies between
Answer:
Dividing and multiplying by we get
,
We know that the max. and minimum value of any cosine is
We know,
We know because value of
is more that
So we replace with
. The above inequality still holds true.
So range of above expression can be