Math, asked by kritika38, 1 year ago

tan inverse 2/11+tan inverse 7/24= tan inverse 1/2

Answers

Answered by saurabhsemalti
1

tan ^{ - 1} (2 \div 11) + tan ^{ - 1} (7 \div 24) = tan ^{ - 1} ((2 \div 11 \:  + 7 \div 24) \div (1 - (2 \div 11)(7 \div 24))) \\  = tan ^{ - 1} (1 \div 2)
this is your answer
Answered by itzAshuu
1

{ \blue{ \tan {}^{ - 1}  \frac{2}{11}  +  \tan {}^{ - 1}  \frac{7}{24}  =  \tan {}^{ - 1}  \frac{1}{2} }}

LHS,

 \tan {}^{ - 1}  \frac{2}{11}  +  \tan {}^{ - 1}  \frac{7}{24}  \\{ \green{ We \: know \: that,}} \\

 {\boxed{\tan {}^{ - 1} x +  \tan {}^{ - 1}  y =  \tan {}^{ - 1}  \frac{x  + y}{1 - xy}}}

 =  \tan {}^{ - 1}   \frac{ \frac{2}{11}  +  \frac{7}{24} }{1 -  \frac{2}{11}  \times  \frac{7}{24} }  \\ =   \tan {}^{ - 1}  \frac{48 + 77}{11 \times 24 - 14}  \\  =  \tan {}^{ - 1}  \frac{125}{250}  \\  =  { \tan }^{ - 1}  \frac{1}{2}

=RHS.

________________Proved....

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