Class 11

Math

Co-ordinate Geometry

Straight Lines

prove

$tan_{−1}(1663 )=sin_{−1}(135 )+cos_{−1}(53 )$

$sin_{−1}(135 )=u⇒sinu=135 $

$⇒cosu=1312 $

$tanu=125 $

$=cos_{−1}(53 )=v⇒cosv=53 $

$sinv=54 $

$tanv=34 $

$tan(u+v)=1−tanutanvtanu+tanv $

$1−125 ×34 125 +34 (3616 )(3663 ) =(1663 )$

$∴u+v=tan_{−1}(1663 )$

$sin_{−1}(135 )+cos_{−1}(53 )=tan_{−1}(1663 )$