Step-by-step Solution
Problem to solve:
$\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cdot\cos\left(x\right)$
Learn how to solve trigonometric equations problems step by step online.
$\csc\left(x\right)+\sin\left(x\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}\cos\left(x\right)$
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation csc(x)+sin(x)=cot(x)cos(x). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Multiplying the fraction by \cos\left(x\right). When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents. The reciprocal sine function is cosecant: \frac{1}{\sin(x)}=\csc(x).
Final Answer
$x=0+2\pi n,\:x=2\pi+2\pi n,\:x=\pi+2\pi n$