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Chapter 7: Q. 106 (page 498)

If z=tan伪2, show that localid="1646416257885" cos伪=1-z21+z2.

Short Answer

Expert verified

To show that cos伪=1-z21+z2,first use double angle and inverse trigonometry, and simplify the equation.

Step by step solution

01

Step 1. Given information.

Consider the given question,

z=tan伪2,cos伪=1-z21+z2

Using the double-angle formula,

cos2胃=2cos2胃-1

From inverse trigonometry,

coscos-1x=x

Then,

tan-1=cos-111+x2

02

Step 2. Simplify the equation.

Consider the given question,

z=tan伪2伪=2tan-1z伪=2cos-111+z2

Using the double-angle formula and inverse trigonometry,

cos伪=cos2cos-111+z2=2cos22cos-111+z2-1=21+z2-1=1-z21+z2

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Most popular questions from this chapter

If tan伪=x+1and role="math" localid="1646425111199" tan尾=x-1,show that

role="math" localid="1646426027733" 2cot(伪-b)=x2

Suppose that f and g are two functions with the same domain. Iff(x)=g(x) for every x in the domain, the equation is called a(n) ____. Otherwise, it is called a(n) _____ equation.

Establish each identity.

1-2cos2胃sin胃cos胃=tan胃-cot胃

If x=2tan胃, express sin2胃as a function ofx.

solve each equation on the interval

3sin胃+cos胃=1
See all solutions

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