Question

(1+ cos x + sin x) / (1+ cos x - sin x) = (1+sin x)/ cos x​

Answer 1

Answer:

LHS

1 + cos x + sin x

----------------------

1 + cos x - sin x

Dividing and multiplying by cos x

sec x + 1 + tan x

= ----------------------

sec x + 1 - tan x

sec x + tan x + sec²x - tan²tan x

= --------------------------------------------

sec x + 1 - tan x

sec x + tan x + (sec x - tan x) (sec x + tan x)

= -----------------------------------------------------------

sec x + 1 - tan x

sec x + tan x(sec x - tan x + 1)

= ----------------------------------------

sec x + 1 - tan x

= sec x + tan x

1 sin x 1 + sin x

1 sin x 1 + sin x = -------- + --------- = ------------

1 sin x 1 + sin x = -------- + --------- = ------------ cos x cos x cos x

Hope it helps☺