Can you please solve this equation?, thanks! cos 2x = 5 sin^2 x - cos^2 x (in terms of cosine x)

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Answer 1 · 2018-04-15T00:22:40

#x=pi/6,(5pi)/6,(7pi)/6,(11pi)/6#

#cos(2x)=5(sinx)^2-(cosx)^2#

#(cosx)^2-(sinx)^2=5(sinx)^2-(cosx)^2#

#2(cosx)^2-1=5(1-(cosx)^2)-(cosx)^2#

#2(cosx)^2-1=5-5(cosx)^2-(cosx)^2#

#8(cosx)^2=6#

#(cosx)^2=3/4#

#cosx=+-sqrt3/2#

#x=pi/6,(5pi)/6,(7pi)/6,(11pi)/6#