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Chapter 7: Q. 12 (page 450)

True or Falsey=tan-1xmeansx=tany,where-鈭�<x<鈭�and-蟺2<y<蟺2

Short Answer

Expert verified

True statement :y=tan-1xmeansx=tany,where-鈭�<x<鈭�and-蟺2<y<蟺2

Step by step solution

01

Step 1. Given Information:

Given Statement:

y=tan-1xmeansx=tany,where-鈭�<x<鈭�and-蟺2<y<蟺2

We want to know is the given statement is True or False.

02

Step 2. Solution:

The tan-1 function is the inverse of the tan function so they cancel each other under predefined conditions.

We know that

  • The range of the function = Domain of the original function.
  • The domain of the inverse = range of the original function.

Applying the tan function both sides of the given expression we get:

tan(y)=tan(tan-1x)

Therefore, we get:

x=tany,where-鈭�<x<鈭�and-蟺2<y<蟺2

Hence, the statements is True.

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