Final answer to the problem
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: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$
Learn how to solve trigonometric identities problems step by step online.
$\frac{\cos\left(x\right)}{1+\sin\left(x\right)}+\frac{\cos\left(x\right)}{1-\sin\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)/(1+sin(x))+cos(x)/(1-sin(x))=2sec(x). 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.. Factor the polynomial \cos\left(x\right)\left(1-\sin\left(x\right)\right)+\cos\left(x\right)\left(1+\sin\left(x\right)\right) by it's greatest common factor (GCF): \cos\left(x\right).