Exercise
$\sec\left(x\right)-\tan\left(x\right)=\frac{\cos\left(x\right)}{1-\sin\left(x\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation sec(x)-tan(x)=cos(x)/(1-sin(x)). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Multiplying the fraction by -1. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.
Solve the trigonometric equation sec(x)-tan(x)=cos(x)/(1-sin(x))
Final answer to the exercise
$x=0+2\pi n,\:x=\pi+2\pi n,\:x=\frac{1}{2}\pi+2\pi n\:,\:\:n\in\Z$