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?

1 Answer
Mar 4, 2018

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

Explanation:

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]