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: $sec (pi/4) = sqrt(2)$

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