One of the following equations work for all values of x, the other does not.sin(x)/csc(x) +cos(x)/sec(x)=1, cos4(x)-sin4(x)=1a) Determine which one was an identity and prove it. b) Explain why the other solution is not an identity.

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Description: One of the following equations work for all values of x, the other does not.sin(x)/csc(x) +cos(x)/sec(x)=1, cos4(x)-sin4(x)=1a) Determine which one was an identity and prove it. b) Explain why the other solution is not an identity.

The first given equation is: sinxcosecx+cosxsecx=1 Solving the Left hand side of equation: 1cosecx=sinx and 1secx=cosx LHS=sinxcosecx+cosxsecx=sinx×1cosecx+cosx×1secx =sinx sinx+ cosx cosx=sin2x+cos2x=1 RHS=1 Since Left hand side of the equation is equal to right hand side, the given identity is proved.The second given equation is: cos4x-sin4x=1 Solving the left hand side of the equation. LHS=cos4x-sin4xApplying the identity a2-b2=a+ba-b LHS=cos2x+sin2xcos2x-sin2x=1×cos2x-sin2x=cos2x RHS= 1 Since left hand side of the equation is not equal to right hand side of the equation , this is not a identity. Thus, cos4x-sin4x=cos2x

Answered: One of the following equations work for…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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One of the following equations work for all values of x, the other does not.

sin(x)/csc(x) +cos(x)/sec(x)=1,

cos⁴(x)-sin⁴(x)=1

a) Determine which one was an identity and prove it.

b) Explain why the other solution is not an identity.

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