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Prove That: Sin X + Sin 2 X 1 + Cos X + Cos 2 X = Tan X

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प्रश्न

Prove that:  \[\frac{\sin x + \sin 2x}{1 + \cos x + \cos 2x} = \tan x\]

 
संख्यात्मक
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उत्तर

\[LHS = \frac{\text{ sin } x + \sin2x}{1 + \text{ cos } x + \cos2x}\]

\[ = \frac{\text{ sin } x + \sin2x}{\text{ cos } x + \left( 1 + \text{ cos } 2x \right)}\]

\[= \frac{\text{ sin } x + 2\text{ sin } x \text{ cos } x}{\text{ cos } x + 2 \cos^2 x} \left[ \because \sin2x = 2\text{ sin } x \text{ cos } x \text{ and  } 2 \cos^2 x = 1 + \cos2x \right]\]

\[= \frac{\text{ sin } x \left( 1 + 2\text{ cos } x \right)}{\text{ cos } x \left( 1 + 2\text{ cos } x \right)}\]

\[ = \text{ tan } x = RHS\]

\[\text{ Hence proved } .\]

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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.1 [पृष्ठ २८]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.1 | Q 6 | पृष्ठ २८

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