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Chapter 7: Q 66. (page 458)

In Problem, write each trigonometric expression as an algebraic expression in u.

tansec-1u

Short Answer

Expert verified

Trigonometric expression tansec-1uas an algebraic expression in u is given byu2-1

Step by step solution

01

Step 1. Given information

An expression istansec-1u.

02

Step 2. Value of the expression in terms of u.

Consider the expression tansec-1u.

sec-1u=xu=secx

Consider the following figure:

Side opposite to angle localid="1646568319186" x=u2-1

So,

localid="1646568327489" tanx=u2-1x=tan-1u2-1

So,

tansec-1u=tantan-1u2-1=u2-1

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