Verify the identity 14 sec2 x 12 sec x 12 sec x choose the

Verify the identity.

1-4 sec^2 x / 1-2 sec x = 1+2 sec x

choose the sequence of steps below that verifies the identity

a) 1-4 sec^2 x / 1-2 sec x= (2-sec x)(2-sec x)/ 1-2 sec x = 1+2 sec x

b) 1-4 sec^2 x / 1-2 sec x= (1-2 sec x)(1-2 sec x)/ 1-2 sec x= 1+2 sec x

c) 1-4 sec^2 x / 1-2 sec x= (2+ sec x) (2- sec x)/ 1-2 sec x= 1+2 sec x

d) 1-4 sec^2 x / 1-2 sec x= (1+2 sec x)(1-2 sec x)/1-2 sec x= 1+2 sec x

Solution

(1-4 sec^2 x) / (1-2 sec x) = 1+2 sec x

LHS : (1-4 sec^2 x) / (1-2 sec x)

= (1 -2secx)(1+2secx)/( 1- 2secx)

= 1+ 2secx

Option d