simplify sin x tan x 1 cos xSolutiona sin x tan x tan x

Solution

a) sin x / tan x

tan x = sin x / cos x

sin x / sin x / cosx

= cos x

b) sec x / csc x

sec x= 1 / cos x

csc x = 1/ sin x

hence we can write

1 / cos x / 1 / sin x = sin x / cos x = tan x

c) ( sin x + tan x ) / ( 1+ cos x )

( sin x + sin x / cos x ) / (1 + cos x )

(sin x cos x + sin x ) / cos x ( 1 + cos x )

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

cancelling out (1+cosx) from top and bottom we get

sin x / cos x = tan x