Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Combine fractions with different denominator using the formula: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$
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$\frac{\cos\left(x\right)-\cos\left(y\right)}{\sin\left(x\right)+\sin\left(y\right)}+\frac{\sin\left(x\right)-\sin\left(y\right)}{\cos\left(x\right)+\cos\left(y\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (cos(x)-cos(y))/(sin(x)+sin(y))+(sin(x)-sin(y))/(cos(x)+cos(y))=0. Starting from the left-hand side (LHS) of the identity. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Solve the product of difference of squares \left(\sin\left(x\right)-\sin\left(y\right)\right)\left(\sin\left(x\right)+\sin\left(y\right)\right).