Question

find the principal and general solution of the following equation sec x=2 .​

Answer 1

Step-by-step explanation:

sec x = 2

pricipal solution...

cos x = 1/2

cos π\3 =1/2

by allied angle formula ...

cos x = cos ( 2π -x )

cos π\3 = cos (2π - π\3 )

= cosc5π\3

hence... π\3 And 5π\3 are the principal solution

general solution

cos x = 1/2

cos π\3 = 1/2

cos x = cos π\3

WKT...

cos (theta ) + cos ( alpha ) , iff (theta) = 2nπ +- (alpha) , where n € z

hence ..

x = 2nπ +-π\3 , n€ z

this is the general solution ...

I hope you understand

I hope you understand please fallow me

Answer 2

Answer:

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secx=2 ⇒ cos x = 1/2 cos x = cos π/3 Using formula for general soluton of cos x = cos y i.e x = 2n π y We have x = 2n π - π/ 3 The solutions that lie in the interval 0 to 2 π , both included are principal solution So they are , in this case , π/3, 2 π- π/ 3 = 5π