Exercise
$\frac{cos^2x+sinx\left(1+sinx\right)}{\left(\cos\left(x\right)\right)^2}=\frac{1}{sinx}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation (cos(x)^2+sin(x)(1+sin(x)))/(cos(x)^2)=1/sin(x). Apply fraction cross-multiplication. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(1+\sin\left(x\right)\right). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Multiplying polynomials \sin\left(x\right) and 1+\sin\left(x\right).
Solve the trigonometric equation (cos(x)^2+sin(x)(1+sin(x)))/(cos(x)^2)=1/sin(x)
Final answer to the exercise
$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$