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This can be achieved by transforming one or both sides of the given equation,

until they look the same.
A) cos^2(x) = 1-sin^2(x)B) sin(x)cos^2+sin^3(x) = sin(x)
c) 1-2cos^2(x) = -1+2sin^2(x)
d) sin(-x)sin(x) = -1+cos^2(x)

User Chry Cheng
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To achieve the desired form for each equation, we'll use various trigonometric identities:

A) cos^2(x) = 1 - sin^2(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

cos^2(x) = cos^2(x)

Both sides of the equation are already in the same form, so no further transformation is needed.

B) sin(x)cos^2(x) + sin^3(x) = sin(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

sin(x)cos^2(x) + sin^3(x) = sin(x)(1 - sin^2(x))

Next, using the distributive property, we can simplify further:

sin(x)cos^2(x) + sin^3(x) = sin(x) - sin^3(x)

Now, both sides of the equation are in the same form.

C) 1 - 2cos^2(x) = -1 + 2sin^2(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

1 - 2cos^2(x) = -1 + 2(1 - cos^2(x))

Simplifying further:

1 - 2cos^2(x) = -1 + 2 - 2cos^2(x)

Now, both sides of the equation are in the same form.

D) sin(-x)sin(x) = -1 + cos^2(x)

Using the identity sin(-x) = -sin(x), we can rewrite the equation as:

-sin(x)sin(x) = -1 + cos^2(x)

Simplifying further:

-sin^2(x) = -1 + cos^2(x)

Now, both sides of the equation are in the same form.

By using the appropriate trigonometric identities and simplifying the expressions, we have achieved the desired form for each equation.

User Daniel Hariri
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