3.Trigonometrical Ratios, Functions and Identities
easy

यदि $\tan A + \cot A = 4,$ तब ${\tan ^4}A + {\cot ^4}A   $ का मान होगा 

A

$110$

B

$191$

C

$80$

D

$194$

Solution

(d) $\tan A + \cot A = 4$ 

$ \Rightarrow \,{\tan ^2}A + {\cot ^2}A + 2\,\tan A\,\,\cot A = 16$

$ \Rightarrow \,{\tan ^2}A + {\cot ^2}A = 14\,\, $

$\Rightarrow \,{\tan ^4}A + {\cot ^4}A + 2 = 196$

$ \Rightarrow \,{\tan ^4}A + {\cot ^4}A = 194.$

Standard 11
Mathematics

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