Complete the identity?

Question

#((tanx+1)(tanx+1)-sec^2x)/tanx = ?#

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Answer 1 · 2018-05-28T04:20:25

#((tanx+1)(tanx+1)-sec^2x)/tanx #

#=((tan^2x+1+2tanx)-sec^2x)/tanx #

#=(sec^2x+2tanx-sec^2x)/tanx #

#=(2tanx)/tanx=2 #

Answer 2 · 2018-05-28T04:26:13

#color(blue)(=> 2#

#((tan x + 1) * ( tan x + 1) - sec ^2 x) / tan x#

#=>( tan x + 1)^2 - sec^2 x)/ tan x#

#=> (color(crimson)(cancel(tan ^2x + 1))+ 2tan x - color(crimson)cancel(sec ^2 x)) / tan x# as

#color(purple)(1 + tan ^2 x = sec ^2 x#, identity

# =>(2 cancel(tan x)) / cancel(tan x)#

#color(blue)(=> 2#