1800-150-456-789
FlagBACK
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

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


Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 2 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available

Last Activity: 3 Years ago