Flag Trigonometry> if x and y are the solutions of 12 sinx +...
question mark

if x and y are the solutions of 12 sinx + 5 cos x= 2 y^2-8y+21, the value of 3864 cot(xy/2) is?

vishnu , 11 Years ago
Grade 12
anser 1 Answers
Rinkoo Gupta

Last Activity: 11 Years ago

LHS=12 sinx+5cosx</ sqrt(144+25)

=12sinx+5cosx</13
LHS</13
RHS=2(y^2-4y)+21
=2(y^2-4y+4)-8+21
=2(y-2)^2+13
hence RHS>/13
Roots of the equation exist if LHS=RHS=13
=> 2y^2-8y+21=13
=>2y^2-8y+8=0
=>y^2-4y+4=0
=>(y-2)^2=0
=>y=2
12sinx+5cosx=13
(12/13)sinx+(5/13)cosx=1
cos@sinx+sin@cosx=1 where @=arctan(5/12)
sin(x+@)=1=sin(pi/2)
x+arctan(5/12)=pi/2
x=pi/2-arctan(5/12)=arccot(5/12)
cotx=5/12
Hence 3864 cot(xy/2)=3864 cotx
=3864(5/12)=1610

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free