cot A + cosec A किसके बराबर है?

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cot A + cosec A किसके बराबर है?

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NDA (Held On: 17 Nov 2019) Maths Previous Year paper

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$\tan (\frac{A}{2})$
$\cot (\frac{A}{2})$
$2 \tan (\frac{A}{2})$
$2 \cot (\frac{A}{2})$

Answer 1

संकल्पना:

cos 2A = cos² A - sin²A = 2 cos² A - 1

sin 2A = 2 sin A × cos A

गणना:

$\Rightarrow \cot A + c o s e c A = \frac{\cos A}{\sin A} + \frac{1}{\sin A}$

$\Rightarrow \cot A + c o s e c A = \frac{1 + \cos A}{\sin A}$

चूँकि हम जानते हैं कि,

cos 2A = cos² A - sin²A = 2 cos² A - 1

$\Rightarrow \cot A + c o s e c A = \frac{1 + \cos A}{\sin A} = \frac{2 \times \cos^{2} (\frac{A}{2})}{\sin A}$

चूँकि हम जानते हैं कि,

sin 2A = 2 sin A × cos A

$\Rightarrow \cot A + c o s e c A = \frac{1 + \cos A}{\sin A}$

$= \frac{2 \times \cos^{2} (\frac{A}{2})}{\sin A} = \frac{2 \times \cos^{2} (\frac{A}{2})}{2 \times \cos (\frac{A}{2}) \times \sin (\frac{A}{2})} = \cot (\frac{A}{2})$

∴ cot A + cosec A का मान $\cot (\frac{A}{2})$ है।

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cot A + cosec A किसके बराबर है?

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