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=14[3sinxsin3x] and cos4(x)=18[3+4cos2x+cos4x]

Explanation:

sin3x=3sinx4sin3x

4sin3x=3sinxsin3x

sin3x=14[3sinxsin3x]

Also, cos4(x)=[2cos2x2]2

=14[1+cos2x]2

=14[1+2cos2x+cos2(2x)]

=18[2+4cos2x+2cos2(2x)]

=18[2+4cos2x+1+cos4x]=18[3+4cos2x+cos4x]