3.Trigonometrical Ratios, Functions and Identities
medium

यदि $\cos A = \cos B\,\,\cos C$ और  $A + B + C = \pi ,$ तो  $\cot \,B\,\cot \,C$ का मान है

A

$1$

B

$2$

C

$\frac{1}{3}$

D

$\frac{1}{2}$

Solution

(d) यहाँ $\cos A = \cos B\cos C$

$A + B + C = \pi  \Rightarrow B + C = \pi  – A$

 $\therefore \cos (B + C) = \cos (\pi  – A) \Rightarrow \cos (B + C) =  – \cos A$

$ \Rightarrow \cos B\cos C – \sin B\sin C =  – \cos B\cos C$

$( \because {\rm{Given}}\cos A = \cos B\cos C)$ 

 $ \Rightarrow 2\cos B\cos C = \sin B\sin C$

$ \Rightarrow \frac{{\cos B\cos C}}{{\sin B\sin C}} = \frac{1}{2}$

$\Rightarrow \cot B\cot C = \frac{1}{2}$.

Standard 11
Mathematics

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