Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Learn how to solve trigonometric identities problems step by step online.
$\frac{\cos\left(x-y\right)}{\cos\left(x\right)\cos\left(y\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x-y)/(cos(x)cos(y))=1+tan(x)tan(y). Starting from the left-hand side (LHS) of the identity. Using the cosine of a sum formula: \cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals y. Expand the fraction \frac{\cos\left(x\right)\cos\left(y\right)+\sin\left(x\right)\sin\left(y\right)}{\cos\left(x\right)\cos\left(y\right)} into 2 simpler fractions with common denominator \cos\left(x\right)\cos\left(y\right). Simplify the resulting fractions.