Prove the trigonometric identity $\frac{1-\cos\left(x\right)}{\sin\left(x\right)}=\frac{\sin\left(x\right)}{1+\cos\left(x\right)}$

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$\frac{\sin\left(x\right)}{1+\cos\left(x\right)}$

Learn how to solve problems step by step online. Prove the trigonometric identity (1-cos(x))/sin(x)=sin(x)/(1+cos(x)). Starting from the right-hand side (RHS) of the identity. Multiply and divide the fraction \frac{\sin\left(x\right)}{1+\cos\left(x\right)} by the conjugate of it's denominator 1+\cos\left(x\right). Multiplying fractions \frac{\sin\left(x\right)}{1+\cos\left(x\right)} \times \frac{1-\cos\left(x\right)}{1-\cos\left(x\right)}. 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..