Step-by-step Solution

Solve the trigonometric equation $\tan\left(2x\right)=1$

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Step-by-step explanation

Problem to solve:

$\tan\left(2x\right)=1$

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

$\frac{\sin\left(2x\right)}{\cos\left(2x\right)}=1$

Unlock this full step-by-step solution!

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation tan(2*x)=1. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiply both sides of the equation by \sin. Multiplying the fraction by \sin\left(x\right). Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right).

Final Answer

$x=0+2\pi n,\:x=\pi+2\pi n,\:x=0$
$\tan\left(2x\right)=1$

Time to solve it:

~ 1.47 s (SnapXam)

Related topics:

Trigonometric Equations