Question #d188c

1 Answer
P dilip_k
Jan 6, 2018

solution #x=20^@ and120^@ #

Explanation:

# tan x = (√3) / (1+4cosx)#

# =>sin x/cosx = (√3) / (1+4cosx)#

#=>sinx+4sinxcosx=sqrt3cosx#

#=>4sinxcosx=sqrt3cosx-sinx#

#=>2sinxcosx=sqrt3/2cosx-1/2sinx#

#=>sin2x=sin60^@cosx-cos60^@sinx#

#=>sin2x=sin(60^@-x)#

#=>2x=60^@-x#

#=>3x=60^@#

#=>x=20^@#

Again #sin2x=sin(60^@-x)#

#=>sin(180-2x)=sin(60^@-x)#

#=>180-2x=60^@-x#

#=>2x-x=180^@-60^@=120^@#

#=>x=120^@#

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