General solution of trigonometric equation tan, x + tan ,2x + tan, 3x = tan ,x · tan, 2x &mid

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Trigonometrical Equations

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The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is

A

$x = n\pi$

B

$n\pi ± \frac{\pi }{3}$

C

$x = 2n\pi$

D

$x = \frac{{n\pi }}{3}$ where $n \in I$

Solution

$tan \,x + tan\, 2x + tan\, 3x = tan \,3x – tan \,2x – tan \,x$

$\Rightarrow tan\, x + tan\, 2x = 0$

$\therefore$ $tan\, 2x = tan\, (- x)$

$2x = n\pi – x$

$x =$ $\frac{{n\pi }}{3}$, $n \in I$

Standard 11

Mathematics

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