Prove the trigonometric identity $\frac{1}{1+\sin\left(x\right)}+\frac{1}{1-\sin\left(x\right)}=2\sec\left(x\right)^2$

Learn how to solve factor by difference of squares problems step by step online.

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

Learn how to solve factor by difference of squares problems step by step online. Prove the trigonometric identity 1/(1+sin(x))+1/(1-sin(x))=2sec(x)^2. 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}. Solve the product of difference of squares \left(1+\sin\left(x\right)\right)\left(1-\sin\left(x\right)\right). Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2.