Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Prove from LHS (left-hand side)
- Prove from RHS (right-hand side)
- Express everything into Sine and Cosine
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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Starting from the left-hand side (LHS) of the identity
Learn how to solve trigonometric identities problems step by step online.
$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2+\left(\sin\left(x\right)-\cos\left(x\right)\right)^2$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)+cos(x))^2+(sin(x)-cos(x))^2=2. Starting from the left-hand side (LHS) of the identity. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Simplify -2\sin\left(x\right)\cos\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x).
