Question

If 2ycos=xSin & 2xSec-yCosec=3 then show that x^2+4y^2=4.​

Answer 1

Step-by-step explanation:

Solution:

x2+4y2= ? .......(A)

Aaccording to question

y Cos$ = x Sin$ .........(given)

this equation can be written as

2y/x=Sin$/Cos$ = k ( say) ,

or, 2y/Sin$=x/Cos$= k

or, 1/Sin$ ×2y = k or , 1/ Cos$ ×X = k

Or, 2y cosec$ = k or, X sec$ =k

or, cosec$ = k/2y .......(1) or, sec$ =k/X....(2)

Since,

2Xsec$ - y cosec$ =3 .........(given)

2X × k/X - y × k/2y =3 ( from equation 1 &2 )

Or, 2k- k/2 =3

Or, (4k-k)/2 = 3

Or, 3k/2=3

Or, 3k = 6

Or, k= 6/3

Or, k=2

now putting the value of "k" in equation 1 & 2 , we get

y= sin$ and X = 2 cos$

Now

rom equation (A)

2 2

X + 4 y = ?

Now,

2 2

LHS= (2cos$) + 4 (sin$)

2 2

= 4Cos $ + 4 Sin $

2 2

= 4( Cos $ + Sin $ )

= 4×1

= 4

Answer 2

Answer:

The answer for this question is

4