Find the General Solution of the Following Equation: Tan M X + Cot N X = 0 - Mathematics

प्रश्न

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]

योग

उत्तर

We have:

\[\tan mx + \cot nx = 0\]

\[\Rightarrow \tan mx = - \cot nx\]

\[ \Rightarrow \tan mx = \tan \left( \frac{\pi}{2} + nx \right)\]

\[ \Rightarrow mx = r\pi + \left( \frac{\pi}{2} + nx \right), r \in Z\]

\[ \Rightarrow (m - n) x = r\pi + \frac{\pi}{2}, r \in Z\]

\[ \Rightarrow x = \left( \frac{2r + 1}{m - n} \right)\frac{\pi}{2}, r \in Z\]

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Trigonometric Equations

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Q 2.08 Q 2.07 Q 2.09

अध्याय 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

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आरडी शर्मा Mathematics [English] Class 11

अध्याय 11 Trigonometric equations
Exercise 11.1 | Q 2.08 | पृष्ठ २१

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Trigonometric Equations

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