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  • <img alt="\\\text { If } \sin (A-B)=\frac{2}{\sqrt{13}}, \sin (A+B)=\frac{4}{\sqrt{17}} \\ what\ is\ the\ value\ of\ \tan 2A" src="/latex-image/?%5C%5C%5Ctext%20%7B%20If%20%7D%20%5Csin%20%28A-B%29%

\\\text { If } \sin (A-B)=\frac{2}{\sqrt{13}}, \sin (A+B)=\frac{4}{\sqrt{17}} \\ what\ is\ the\ value\ of\ \tan 2A

(Given that A+B and A-B are acute angles)

Option: 1

\frac{14}{5}


Option: 2

\frac{5}{14}


Option: 3

-\frac{5}{14}


Option: 4

-\frac{14}{5}


Answers (1)

best_answer

\\\text { If } \sin (A-B)=\frac{2}{\sqrt{13}}, \sin (A+B)=\frac{4}{\sqrt{17}} \\ \tan(A+B)=4,\ \tan(A-B)=\frac{2}{3}\\ \tan 2A= \tan[(A+B)+(A-B)]=\frac{ \tan (A+B)+\tan (A-B)}{1-\tan (A+B) \tan (A-B)}\\ =\frac{4+\frac{2}{3}}{1-4* \frac{2}{3}}\\ =-\frac{14}{5}

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shivangi.shekhar

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