Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Apply the trigonometric identity: $\sin\left(a\right)+\sin\left(b\right)$$=2\sin\left(\frac{a+b}{2}\right)\cos\left(\frac{a-b}{2}\right)$, where $a=9x$ and $b=x$
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$\frac{\sin\left(10x\right)}{\sin\left(9x\right)+\sin\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(10x)/(sin(9x)+sin(x))=cos(5x)/cos(4x). Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: \sin\left(a\right)+\sin\left(b\right)=2\sin\left(\frac{a+b}{2}\right)\cos\left(\frac{a-b}{2}\right), where a=9x and b=x. Apply the trigonometric identity: \sin\left(nx\right)=2\sin\left(\frac{n}{2}x\right)\cos\left(\frac{n}{2}x\right), where n=10. Simplify the fraction \frac{2\sin\left(5x\right)\cos\left(5x\right)}{2\sin\left(5x\right)\cos\left(4x\right)} by \sin\left(5x\right).