Step-by-step Solution

Prove the trigonometric identity $\sin\left(x\right)^2-\sin\left(y\right)^2=\cos\left(y\right)^2-\cos\left(x\right)^2$

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Step-by-step Solution

Problem to solve:

$\sin^2\left(x\right)-\sin^2\left(y\right)=\cos^2\left(y\right)-\cos^2\left(x\right)$

Solving method

Learn how to solve trigonometric identities problems step by step online.

$1-\cos\left(x\right)^2-\sin\left(y\right)^2=\cos\left(y\right)^2-\cos\left(x\right)^2$

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)^2-sin(y)^2=cos(y)^2-cos(x)^2. Applying the trigonometric identity: \sin^2(\theta)=1-\cos(\theta)^2. Applying the trigonometric identity: \sin^2(\theta)=1-\cos(\theta)^2. Solve the product -(1-\cos\left(y\right)^2). Since both sides of the equality are equal, we have proven the identity.

Final Answer

true
$\sin^2\left(x\right)-\sin^2\left(y\right)=\cos^2\left(y\right)-\cos^2\left(x\right)$

Related Formulas:

1. See formulas

Time to solve it:

~ 0.71 s