Question

write the trigonometric expression as an algebraic expression containing u and v. Give the restrictions required on u and v.

Answer 1

Step 1:

The trigonometric expression  is 

Consider,

in the interval .

.

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

.

.

Step 2:

Consider,

in the interval .

.

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

.

Step 3:

Substitute and in trigonometric expression.

From difference formula of trigonometric function : .

Substitute these values in above expression.

                                             

.

Solution :

in the intervals and .