Question

Verify the trig identity (1/2)sin4x = 2sinxcosx - 4(sin^3)xcosx


No cross multiply. Must use trig identities.

Answer 1

I've got:
1/2sin4x = 2sinxcosx(1-2sin^2x)

1/2sin4x = sin2x(cos^2x)

Answer 2

Okay your first step was perfect... in second step check again that cos^2 x term... you did a mistake there

Answer 3

Recall that \(\sin^2 x= 1 - \cos^2 x\) .. make sure you didn't make any calculation mistake

Answer 4

Ah right. That should be cos2x.

Answer 5

Great! So we have... sin (2x) cos (2x)

Answer 6

Multiply and divide by 2

Answer 7

I don't understand that step.

Answer 8

Okay so we have..

sin(2x)cos(2x)

I multiply with 2 and divide by 2 ...

1/2 * 2 * sin(2x) * cos(2x)

= 1/2 * [2* sin(2x)*cos(2x)]

The term in square brackets seem familiar?

Answer 9

Ah, OK that makes sense. Should it be 2 * (sin(2x)*cos(2x)) though?

Answer 10

Yeah.. 2 * sin(2x) * cos(2x) you can write as sin(4x)