Solve 2 cos x + sec x = 3 ?

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Answer 1 · 2018-04-15T23:45:49

See below

#2cosx+secx=3#

Remember: #secx=1/cosx#

Multiply both sides by #cosx#:
#cosx(2cosx+1/cosx)= 3(cosx)#

#2cos^2x+1= 3cosx#

Solve like a quadratic:
#2cos^2x-3cosx+1=0#

#2cos^2x-2cosx-cosx+1=0#

#2cosx(cosx-1)-1(cosx-1)=0#

#cosx-1=0#

#2cosx-1=0#

#cosx=1#
#x= 0#

#cosx=1/2#
#x= pi/3, (5pi)/3#

General Solutions:
#x=0+2pin#
#x=pi/3+2pin#
#x=(5pi)/3+2pin#
Where n is an element of all integers

graph{2cosx+secx-3 [-5.985, 14.015, -5.73, 4.27]}