Use double-angle identities to verify that sin(4x) = 4 sinx cosx(1 − 2sin2x.

Step-by-step explanation:

In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx

sin2x = 2sinxcosx ... 1

Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;

sin(4x) = sin(2x+2x)

= sin2xcos2x+cox2xsin2x

sin4x = 2sin2xcos2x ..2

also cos2x = cos(x+x) = cosxcox-sinxsinx

cos 2x = cos²x - sin²x ...3

Substituting equation 1 and 3 into 2, we will have;

sin4x = 2(2sinxcosx(cos²x - sin²x ))

sin4x = 4sinxcosx(cos²x - sin²x )

From sin²x+cos²x =1; cos²x = 1-sin²x

Substituting the expression into the resulting equation will give;

sin4x = 4sinxcosx(1-sin²x - sin²x )

sin4x = 4sinxcosx(1-2sin²x) Verified!  

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: