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

2 Answers

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

Explanation:

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

Jan 22, 2018

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#