# What is the proof for 2sin2θ - 1 = sin2θ - cos2θ?

• Veronica_Oles
In summary, the given equation is 2sin2θ - 1 = sin2θ - cos2θ. The left side can be simplified to sin2θ, but the right side cannot be simplified any further. The identities used in this problem are the double angle identity for sine and the identity cos2θ = 1 - sin2θ.

## Homework Statement

2sin2θ - 1 = sin2θ - cos2θ

## The Attempt at a Solution

I am unsure of how to prove these.

So far all I have is

Left side= 2sin2θ - 1
=sin2sin2-1

And I know that right side is equal to 1.

But otherwise not sure where to go from there.

Veronica_Oles said:

## Homework Statement

2sin2θ - 1 = sin2θ - cos2θ

## The Attempt at a Solution

I am unsure of how to prove these.

So far all I have is

Left side= 2sin2θ - 1
=sin2sin2-1

And I know that right side is equal to 1.

But otherwise not sure where to go from there.
The right side is not 1.

2x2 ≠ x2⋅x2 .

So certainly, 2sin2θ ≠ sin2θ ⋅sin2θ

SammyS said:
The right side is not 1.

2x2 ≠ x2⋅x2 .

So certainly, 2sin2θ ≠ sin2θ ⋅sin2θ
I see where I went wrong now.

SammyS said:
The right side is not 1.

2x2 ≠ x2⋅x2 .

So certainly, 2sin2θ ≠ sin2θ ⋅sin2θ
Would I change right side to sin^2x - 1 - sin^2x?

Veronica_Oles said:

## Homework Statement

2sin2θ - 1 = sin2θ - cos2θ

## The Attempt at a Solution

I am unsure of how to prove these.

So far all I have is

Left side= 2sin2θ - 1
=sin2sin2-1

And I know that right side is equal to 1.

But otherwise not sure where to go from there.

Veronica_Oles said:
Would I change right side to sin^2x - 1 - sin^2x?
It's much simpler than this, and there is no need whatever for double-angle identies. What identities do you already know?

## 1. What are Trigonometric Identities?

Trigonometric identities are mathematical equations that involve trigonometric functions, such as sine, cosine, and tangent, and are true for all values of the variables. They are used to simplify complex trigonometric expressions and solve equations involving trigonometric functions.

## 2. Why are Trigonometric Identities important?

Trigonometric identities are important because they allow us to manipulate and simplify trigonometric equations, making them easier to solve. They also help us to establish relationships between different trigonometric functions, which can be useful in various applications in mathematics, science, and engineering.

## 3. How do you prove Trigonometric Identities?

Trigonometric identities can be proven using various methods, such as algebraic manipulation, using trigonometric identities themselves, or using geometric proofs. The key is to manipulate the equations until they are equivalent to each other, and then show that they are true for all values of the variables.

## 4. What are the most commonly used Trigonometric Identities?

Some of the most commonly used trigonometric identities include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. These identities are used in a variety of trigonometric equations and applications.

## 5. How can I remember all the Trigonometric Identities?

One way to remember trigonometric identities is to practice using them regularly. You can also create flashcards or mnemonic devices to help you remember them. It can also be helpful to understand the basic principles and patterns behind the identities, rather than just memorizing them.