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Chapter 5: Q. 27 (page 464)

Write sin(2cos-1x)as an algebraic function.

Short Answer

Expert verified

The given expression as an algebraic function is2x1-x2.

Step by step solution

01

Step 1. Given Information.

The given trigonometric expression issin(2cos-1x).

02

Step 2. Write the given expression as an algebraic function.

To write the given expression as an algebraic function, let 胃=cos-1x.

As we know, cos=bh,here role="math" b=xandh=1.

By using Pythagoras theorem,

h2=b2+p212=x2+p21-x2=p

Now,

sin2胃=2sin胃cos胃=21-x21x1=2x1-x2

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(c) True or False: The substitution x = 2 tan u is a suitable choice for solving鈭�1x2+4dx.

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(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form x2鈭�a2.

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