Question

If 2ycos = xsin and 2xsec ycosec = 3 then the value of x2 + 4y2 is

Answer 1

Answer:

3.......hope it helps

Answer 2

Answer:

x^2 + 4y^2 = 4

Step-by-step explanation:

2ycosa = xsina

2y/x = sina/cosa

let 2y/x = sina/cosa = z

2y/sina = x/cosa = z

2ycoseca = xseca = z

coseca = z/2y and seca = z/x

Given: 2xseca - ycoseca = 3

=> 2x(z/x) - y(z/2y) = 3

=> 2z - z/2 = 3

=> 4z - z = 6

=> z = 2

=> coseca = 2/2y

=> y = sina

=> seca = 2/x

=> x = 2cosa

=> x^2 + 4y^2 = (2cosa)^2 + 4(sina)^2

=> 4cos^2a + 4sin^2a = 4(cos^2a + sin^2a)

Trig identity: cos^2a + sin^2a = 1

=> 4(1) = 4.

Therefore x^2 + 4y^2 = 4