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If 2tan^2 x-sec x=1 which of the following are true? select all that apply

Asec x=1
Bsec x=3
Ctan x=3
Dtan x=-1
Esec x=3/2

Verified Answer :

Answer:

option e) secx = 3/2

Step-by-step explanation:

Given that

\(2tan^2 x-sec x=1\)

Let us write tan square in terms of sec square using the identity that

\(1+tan^2 x =sec^2 x\)

Substitute for tan square

\(2(sec^2 x -1)-secx =1\\2sec^2x-secx-3=0\\(2secx-3)(secx+1)=0\\\)

Equate each factor to 0 to get

sec x = -1 or sec x = 1.5

When sec x =-1, x =180 and tanx =0

Hence correct options is only

option e) secx = 3/2

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