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Find the General Solution of the Following Equation: Sin X = Tan X

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प्रश्न

Find the general solution of the following equation:

\[\sin x = \tan x\]
बेरीज
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उत्तर

We have:

\[\sin x = \tan x\]
\[\Rightarrow \sin x - \tan x = 0\]
\[ \Rightarrow \sin x - \frac{\sin x}{\cos x} = 0\]
\[ \Rightarrow \sin x \left( 1 - \frac{1}{\cos x} \right) = 0\]
\[ \Rightarrow \sin x (\cos x - 1) = 0\]
\[\Rightarrow \sin x = 0\] or
\[\cos x - 1 = 0\]
Now,  
\[\sin x = 0 \Rightarrow x = n\pi, n \in Z\]

\[\cos x - 1 = 0 \]

\[ \Rightarrow \cos x = 1 \]

\[ \Rightarrow \cos x = \cos0 \]

\[ \Rightarrow x = 2m\pi, m \in Z\]

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

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 2.11 | पृष्ठ २१

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