Step-by-step Solution

Solve the trigonometric equation $\frac{1-\sec\left(x\right)}{\tan\left(x\right)}+\frac{\tan\left(x\right)}{1-\sec\left(x\right)}=-2\csc\left(x\right)$

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Step-by-step explanation

Problem to solve:

$\frac{1-\sec\left(x\right)}{\tan\left(x\right)}+\frac{\tan\left(x\right)}{1-\sec\left(x\right)}=-2\csc\left(x\right)$

Learn how to solve trigonometric equations problems step by step online.

$\frac{1-\sec\left(x\right)}{\tan\left(x\right)}+\frac{\tan\left(x\right)}{1-\sec\left(x\right)}+2\csc\left(x\right)=0$

Unlock this full step-by-step solution!

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation (1-sec(x))/(tan(x)+(tan(x)/(1-sec(x))=-2csc(x). Grouping terms. Combine \frac{1-\sec\left(x\right)}{\tan\left(x\right)}+\frac{\tan\left(x\right)}{1-\sec\left(x\right)}+2\csc\left(x\right) in a single fraction. 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}. Multiply -1 times [b].

Final Answer

$x=\mathrm{arcsec}\left(0\right),\:x=\pi $

Problem Analysis

$\frac{1-\sec\left(x\right)}{\tan\left(x\right)}+\frac{\tan\left(x\right)}{1-\sec\left(x\right)}=-2\csc\left(x\right)$

Related formulas:

1. See formulas

Time to solve it:

~ 8.97 seconds