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Chapter 7: Q.29 (page 473)

Establish the identity:(sec(胃)-tan(胃))(sec(胃)+tan(胃))=1

Short Answer

Expert verified

We establish the identity(sec(胃)-tan(胃))(sec(胃)+tan(胃))=1

Step by step solution

01

Given information

We are given an expression(sec(胃)-tan(胃))(sec(胃)+tan(胃))

02

Use algebraic formula (a-b)(a+b)=a2-b2

We get

(sec(胃)-tan(胃))(sec(胃)+tan(胃))=sec2(胃)-tan2(胃)Weknowthat1+tan2(胃)=sec2(胃)sec2(胃)-tan2(胃)=1

03

Conclusion

We establish the identity(sec(胃)-tan(胃))(sec(胃)+tan(胃))=1

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