Solving the Equation: (sinθ + cosθ)2 = 1 + 2sinθ cosθ

  • Thread starter Veronica_Oles
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In summary, the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ is a trigonometric identity used for simplifying expressions and solving equations involving sine and cosine functions. This can be done by using algebraic manipulation and the Pythagorean identity (sin2θ + cos2θ = 1). The Pythagorean identity is a fundamental identity in trigonometry that states sin2θ + cos2θ = 1. It can also be used to solve trigonometric equations by manipulating the equation and isolating the variable. An example of this would be solving the equation sinθ + cosθ = 3/5 for θ.
  • #1
Veronica_Oles
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Homework Statement


(sinθ + cosθ)2 = 1 + 2sinθ cosθ

Homework Equations

The Attempt at a Solution


Would I have to foil out the left side?
 
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  • #2
Veronica_Oles said:

Homework Statement


(sinθ + cosθ)2 = 1 + 2sinθ cosθ

Homework Equations

The Attempt at a Solution


Would I have to foil out the left side?
Why don't you try it? After all, you should be able to expand the square of a binomial expression rather easily.
 

Related to Solving the Equation: (sinθ + cosθ)2 = 1 + 2sinθ cosθ

1. What is the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ?

The equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ is a trigonometric identity that is used to simplify expressions and solve equations involving sine and cosine functions.

2. How do you solve the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ?

To solve the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ, you can use algebraic manipulation and the Pythagorean identity (sin2θ + cos2θ = 1) to simplify the expression and find the values of θ that satisfy the equation.

3. What is the Pythagorean identity?

The Pythagorean identity states that for any angle θ, sin2θ + cos2θ = 1. It is derived from the Pythagorean theorem in geometry and is a fundamental identity in trigonometry.

4. How do you use the Pythagorean identity to solve trigonometric equations?

The Pythagorean identity can be used to simplify expressions and solve equations involving trigonometric functions. By manipulating the equation using the Pythagorean identity, you can often isolate the variable and find the values of θ that satisfy the equation.

5. Can you provide an example of using the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ to solve a problem?

Yes, an example of using the equation (sinθ + cosθ)2 = 1 + 2sinθ cosθ would be solving the equation sinθ + cosθ = 3/5 for θ. By squaring both sides and using the Pythagorean identity, you can simplify the equation to 1 + 2sinθ cosθ = 9/25. From there, you can use algebra to solve for θ.

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