Question

Q6 Q1.) Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Answer 1

16sin^2(x)cos^2(x)
= 16sin^2(x)(1-sin^2(x))
= 16sin^2(x) - 16sin^4(x)
w/ 2nd n 4th power reduction forumla of sine
= 16(1-cos(2x))/2 - 16(3-4cos2x+cos4x)/8
= 8(1-cos(2x)) - 2(3-4cos2x+cos4x)
= 8 - 6 - 8cos2x + 8cos2x - 2cos4x
= 2 - 2cos4x

Answer 2

Using sin2A=2sinAcosB and sin^2A=[1-cos(2A)]/2

16sin^2(x)cos^2(x) = 4[(2sin(x)cos(x)][2sin(x)cos(x)]

=4sin^2(2x)

=2(1-cos4x)