Verify the identity.

cos 4x + cos 2x = 2 - 2 sin2 2x - 2 sin2 x

The equation Cos4x-cos2x = 2 - 2sin²2x - 2sin²x is TRUE

Step-by-step explanation:

To simplify the trigonometry identity

cos 4x + cos 2x, we use the double angle formula .

According to double angle formula,

Cos2A = cos(A+A)

= CosAcosA-SinASinA

= cos²A - Sin²A

= (1-sin²A)-Sin²A

= 1-2sin²A

Similarly, Cos4x = cos(2x+2x)

= cos²2x - sin²2x... (1)

Since cos²2x+Sin²2x = 1

Cos²2x = 1-sin²2x...(2)

Substituting eqn 2 in 1, we have;

Cos4x= (1-sin²2x) - sin²2x

Cos4x = 1 - 2sin²2x... (3)

Similarly for Cos2x;

Cos2x = cos²x-sin²x

Cos2x = (1-sin²x)-sin²x

Cos2x = 1 - 2sin²x...(4)

Cos4x + cos2x = 1 - 2sin²2x +(1-2sin²x)

= 1 - 2sin²2x + 1 - 2sin²x

= 2 - 2sin²2x - 2sin²x

Which proves the equation;

Cos4x-cos2x = 2 - 2sin²2x - 2sin²x

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?