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simplify the expression tan (3 x+ 2pi) as the tangent of a single angle

Simplify The Expression Tan 3 X 2pi As The Tangent Of A Single Angle class=

Sagot :

tan(3x)

Explanation

[tex]\tan (3x+2\pi)[/tex]

Step 1

remember some property

[tex]\tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}[/tex]

then

[tex]\begin{gathered} \tan (3x+2\pi)=\frac{\tan 3x+\tan 2\pi}{1-\tan 3x\tan 2\pi}\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=\frac{\tan 3x+0}{1-\tan 3x\cdot0}\text{ } \\ \tan (3x+2\pi)=\frac{\tan \text{ 3x}}{1-0}=\frac{\tan \text{ 3x}}{1} \\ \tan (3x+2\pi)=\tan (3x) \end{gathered}[/tex]

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