tRiG/ AlGeBrA
posted by CHEYANNE on .
1) Use doubleangle identities to write the following expression, using trigonometric functions of x instead of 4x.
cos 4x
2) Use halfangle identities to write the following expression, using trigonometric functions of x instead of x/4.
sin x/4

cos(4x) = 2cos^2(2x)1
cos2x = 2cos^2(x)  1
cos(4x) = 2(2cos^2(x)1)^2  1
= 2(4cos^4(x)  4cos^2(x)+1)  1
= 8cos^4(x)  8cos^2(x) + 1
or,
sin^4(x) + cos^4(x) 6 sin^2(x)cos^2(x)
or a bunch of other expressions
cos(x/2) = sqrt[(1 + cos(x))/2
sin(x/4) = sqrt[(1  cos(x/2))/2)
= sqrt([1(sqrt[(1+cos(x))/2)]/2)