- #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?
Why don't you try it? After all, you should be able to expand the square of a binomial expression rather easily.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?
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.
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.
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.
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.
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.