Solve the Following Equation For X: `2tan^-1(Sinx)=Tan^-1(2sinx),X!=Pi/2` - Mathematics

प्रश्न

Solve the following equation for x:

$2 \tan^{- 1} (\sin x) = \tan^{- 1} (2 \sin x), x \neq \frac{π}{2}$

उत्तर

$2 \tan^{- 1} (\sin x) = \tan^{- 1} (2 \sin x), x \neq \frac{π}{2}$

$\Rightarrow \tan^{- 1} (\frac{2 \sin x}{1 - \sin^{2} x}) = \tan^{- 1} (2 \sin x)$ $[∵ 2 \tan^{- 1} x = \tan^{- 1} (\frac{2 x}{1 - x^{2}})]$

$\Rightarrow \frac{2 \sin x}{1 - \sin^{2} x} = 2 \sin x$

$\Rightarrow 2 \sin x = 2 \sin x - 2 \sin^{3} x$

$\Rightarrow 2 \sin^{2} x = 0$

$\Rightarrow \sin x = 0$

$\Rightarrow x = 0$

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Inverse Trigonometric Functions (Simplification and Examples)

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Q 8.4 Q 8.3 Q 8.5

अध्याय 4: Inverse Trigonometric Functions - Exercise 4.14 [पृष्ठ ११६]

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अध्याय 4 Inverse Trigonometric Functions
Exercise 4.14 | Q 8.4 | पृष्ठ ११६

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Solve the Following Equation For X: $2 \tan^{- 1} (Sin x) = {Tan}^{- 1} (2 \sin x), X \neq \frac{Π}{2}$ - Mathematics

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Solve the Following Equation For X: 2tan-1(Sinx)=Tan-1(2sinx),X≠Π2 - Mathematics

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Solve the Following Equation For X: $2 \tan^{- 1} (Sin x) = {Tan}^{- 1} (2 \sin x), X \neq \frac{Π}{2}$ - Mathematics

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