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  • If tan⁡α=1/7,tan⁡β=1/3 then cos 2α is equal to A. sin 2β B. sin 4β C. sin 2β D. cos 2β

If \tan \alpha =\frac{1}{7} , \tan \beta =\frac{1}{3} \\\\  then \cos 2 \alpha     is equal to

A. \sin 2 \beta    

B. \sin 4 \beta   

C. \sin 2 \beta

D. \cos 2 \beta

Answers (1)

The answer is the option (b). 

\\\\\\ \tan \alpha =\frac{1}{7} \\\\ \tan \beta =\frac{1}{3} \\\\ \cos 2 \alpha =\frac{1 - \tan ^{2} \alpha }{1+\tan ^{2} \alpha }=\frac{1 - \frac{1}{49}}{1+\frac{1}{49}}=\frac{24}{25} \\\\ \tan 2 \beta =\frac{2\tan \beta }{1 - \tan ^{2} \beta }=\frac{2 \times \frac{1}{3}}{1 - \frac{1}{9}}=\frac{3}{4} \\\\
 \\ \sin 4 \beta =\frac{2\tan 2 \beta }{1+\tan ^{2}2 \beta }=\frac{2 \times \frac{3}{4}}{1+ \left( \frac{3}{4} \right) ^{2}}=\frac{24}{25} \\\\ \cos 2 \alpha =\sin 4 \beta =\frac{24}{25} \\\\

Hence, correct option is (b).

Posted by

infoexpert21

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