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