Question

if (5cosX+ 12sinX = 13) then prove that tanX=12​

Answer 1

$\huge\color{pink}\boxed{\colorbox{Black}{❥ Answer}}$

(5sinx+12siny)

2

+(5cosx+12cosy)

2

=169+120cos(x−y)

(5sinx+12siny)

2

+169=169+120cos(x−y)

(5sinx+12siny)

2

=120cos(x−y)

(5sinx+12siny)=

120cos(x−y)

This is maximum when cos(x−y) is maximum, which is 1 or (x=y)

5cosx+12cosx=13

cosx=

17

13

which is possible.

Hence,

5sinx+12siny=

120

is the maximum value