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Exercise 2.8

Find an alternative expression for ( tan ⁡ x + cot ⁡ x ) 2 .

Solution:

The expression here is the square of the length of the line segment AC. By the Pythagorean Theorem, that is the sum of the squares of the lengths of the sides, OA and OB, or ( csc ⁡ x ) 2 + ( sec ⁡ x ) 2 . I suppose there are lots of other expressions for it as well.

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