How do you simplify #cos4theta-3tan2theta+sin2theta# to trigonometric functions of a unit #theta#?

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Answer 1 · 2016-07-21T15:15:12

#cos4theta-3tan2theta+sin2theta#

#=1-2sin^2 2theta-3tan2theta+sin2theta#

#=1-2sin^2 2theta +sin2theta-3tan2theta#

#=1+2sin2theta-sin2theta-2sin^2 2theta-3tan2theta#

#=(1+2sin2theta)-sin2theta(1+2sin2theta)-3tan2theta#

#=(1+2sin2theta)(1-sin2theta)-3tan2theta#

#=(1+(4x)/(1+x^2))(1-(2x)/(2+x^2))-(6x)/(1-x^2)#

#color(red)("where " x=tantheta)#