Prove #cos(x)+sin(x)tan(x)=sec(x)#?

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Answer 1 · 2018-01-22T12:27:04

#cos(x)+sin(x)sin(x)/cos(x)# (since #tan x =sinx/cosx#)

#cos(x)+(sin^2x/cosx)#
Taking lcm,
#(cos^2x + sin^2x)/cosx#
#=1/cos (x)# (since #cos^2x+sin^2x =1#)
#=secx#
Hence proved

Answer 2 · 2018-01-22T12:27:06

RHS:

#secx=1/cosx#

LHS:

#cosx+sinxtanx#

#=cosx+sinx(sinx/cosx)#

#=cosx+(sin^2x)/cosx#

#=(cosx*cosx)/(1*cosx)+(sin^2x)/cosx#

#=(cos^2x)/(cosx)+(sin^2x)/cosx#

#=(cos^2x+sin^2x)/cosx#

#sin^2x+cos^2x-=1#

#=1/cosx#

#=secx#

#LHS=RHS#