मराठी

Solve the Following Equation: Tan 2 X + ( 1 − √ 3 ) Tan X − √ 3 = 0

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प्रश्न

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]
बेरीज
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उत्तर

\[\tan^2 x + (1 - \sqrt{3}) \tan x - \sqrt{3} = 0\]\[\Rightarrow \tan^2 x + \tan x - \sqrt{3} \tan x - \sqrt{3} = 0\]
\[ \Rightarrow \tan x (\tan x + 1) - \sqrt{3} (\tan x + 1) = 0\]
\[ \Rightarrow (\tan x - \sqrt{3}) (\tan x + 1) = 0\]
\[\Rightarrow (\tan x - \sqrt{3}) = 0\] or
\[(\tan x + 1) = 0\]
Now,
\[\tan x - \sqrt{3} = 0 \]
\[ \Rightarrow \tan x = \sqrt{3} \]
\[ \Rightarrow \tan x = \tan \frac{\pi}{3} \]
\[ \Rightarrow x = n\pi + \frac{\pi}{3}, n \in Z\]
And,
\[\tan x = - 1 \]
\[ \Rightarrow \tan x = \tan\left( - \frac{\pi}{4} \right) \]
\[ \Rightarrow x = m\pi - \frac{\pi}{4}, m \in Z\]
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पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 3.5 | पृष्ठ २२

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