How do you verify the identity #(tan x + cos x) /( 1+sin x )= sec x#?

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Answer 1 · 2015-08-12T13:22:06

# (tan x + cos x)/(1+sin x) ne sec x #

Assuming that # (tan x + cos x)/(1+sin x) = sec x #, it needs to be true for all #x#

Taking # x = pi/4 #:

LHS: # (tan (pi/4) + cos (pi/4))/(1 + sin (pi/4)) = (1+1/sqrt(2))/(1+1/sqrt(2)) = 1 #

RHS: # sec (pi/4) = sqrt(2) #

Answer 2 · 2015-08-12T13:24:13

You can't because # (tan x + cos x)/(1+sin x) ne sec x #

Assuming that # (tan x + cos x)/(1+sin x) = sec x #, it needs to be true for all #x#

Taking # x = pi/4 #:

LHS: # (tan (pi/4) + cos (pi/4))/(1 + sin (pi/4)) = (1+1/sqrt(2))/(1+1/sqrt(2)) = 1 #

RHS: # sec (pi/4) = sqrt(2) #