Solve the Following Equation: Sin X Tan X – 1 = Tan X – Sin X - Mathematics

Question

Solve the following equation:
sin x tan x – 1 = tan x – sin x

Sum

Solution

\[\sin x \tan x - 1 = \tan x - \sin x\]
\[ \Rightarrow \sin x \tan x - \tan x + \sin x - 1 = 0\]
\[ \Rightarrow \tan x\left( \sin x - 1 \right) + 1\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \left( \tan x + 1 \right)\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \left( \tan x + 1 \right) = 0\text{ or }\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \tan x = - 1\text{ or }\sin x = 1\]
\[ \Rightarrow \tan x = \tan\frac{3\pi}{4}\text{ or }\sin x = \sin\frac{\pi}{2}\]
\[ \Rightarrow x = n\pi + \frac{3\pi}{4}\text{ or }x = n\pi + \left( - 1 \right)^n \frac{\pi}{2}, n \in \mathbb{Z}\]

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Trigonometric Equations

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Q 7.8 Q 7.7 Q 7.9

Chapter 11: Trigonometric equations - Exercise 11.1 [Page 22]

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RD Sharma Mathematics [English] Class 11

Chapter 11 Trigonometric equations
Exercise 11.1 | Q 7.8 | Page 22

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