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What is the general solution of tan5x-tan3x=0? -_ _ _ _ _ _ _ _ _ _ _

What is the general solution of tan5x-tan3x=0? -_ _ _ _ _ _ _ _ _ _ _ 

Grade:11

1 Answers

Sujit Kumar
111 Points
5 years ago
Here is the solution...
tan5x-tan3x=0
\rightarrow \frac{sin5x}{cos5x}-\frac{sin3x}{cos3x}=0
\rightarrow \frac{sin5xcos3x-sin3xcos5x}{cos3x.cos5x}=0
\rightarrow \frac{sin(5x-3x)}{cos3x.cos5x}=0
\rightarrow sin2x=0
      (sin0=0)
\rightarrow sin2x=sin0
 
WE KNOW:
 sinx=siny\rightarrow x=n\pi +(-1)^{n}y
 
\rightarrow x=n\pi +(-1)^{n}.0
\rightarrow x=n\pi                           where\ (n\in Z)
Hope it’s clear!

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