Final Answer
Step-by-step Solution
Specify the solving method
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
Learn how to solve trigonometric identities problems step by step online.
$\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)/(1+sin(x))=sec(x)-tan(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 . Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2. Simplify the fraction by \cos\left(x\right).