How do I rewrite the following two trig expressions with exponents no greater than 1? Such as (A) (Sin^3)x (B) (cos^4)x?

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Answer 1 · 2018-03-04T05:38:45

#sin3x=1/4[3sinx-sin3x]# and #cos^4(x)=1/8[3+4cos2x+cos4x]#

#rarrsin3x=3sinx-4sin^3x#

#rarr4sin^3x=3sinx-sin3x#

#rarrsin^3x=1/4[3sinx-sin3x]#

Also, #cos^4(x)=[(2cos^2x)/2]^2#

#=1/4[1+cos2x]^2#

#=1/4[1+2cos2x+cos^2(2x)]#

#=1/8[2+4cos2x+2cos^2(2x)]#

#=1/8[2+4cos2x+1+cos4x]=1/8[3+4cos2x+cos4x]#