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