How do you verify? Tan x + cos x = sin x (sec x + cotan x)

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Answer 1 · 2018-02-20T16:05:11

Please see below.

#LHS=tanx+cosx#

#=sinx/cosx+cosx#

#=sinx(1/cosx+cosx/sinx)#

#=sinx(secx+cotx)=RHS#

Answer 2 · 2018-02-20T16:06:42

See the proof below

We need

#secx=1/cosx#

#tanx=sinx/cosx#

#cotx=cosx/sinx#

Therefore,

#LHS=tanx+cosx#

#=sinx/cosx+cosx#

#=sinx(1/cosx+cosx/sinx)#

#=sinx(secx+cotx)#

#=RHS#

#QED#