Verify the identity cos x cos x tan2 x sec x Choose the se

Verify the identity cos x + cos x tan^2 x - sec x Choose the sequence of steps below that verifies the identity: cos x + cos x tan^2 x = cos x(1 + tan^2 x) = 1/sec^2 x - sec x = sec x cos x + cos x tan^2 x = cos x(1 + tan^2 x) = 1/sec x - sec^2 x = sec x cos x + cos x tan^2 x = cos x(tan^2 x - 1) = 1/sec x - sec x^2 = sec x cos x + cos x tan^2 x = 1 + tan^2 x = sec x

Solution

cos x+ cos x*tan²x = sec x

steps given in option B verify the identity as:

LHS:

cos x+ cos x*tan²x =   cos x [ 1 + tan²x]

= cosx*sec²x [ from sec²x - tan²x = 1]

= ( 1/sec x)* sec² x [ cos x = 1/ sec x]

= sec x

= RHS

LHS = RHS