Question

If x = cosec A +cos A and y = cosec A-cos A then prove that(
2/x+y)^2+(x-y/2)^2-1=0​

Answer 1

Step-by-step explanation:

add x and y

x=cosec A+cos A

y=cosec A-cos A

--------------------------

x+y=2cosec A

x+y/2=cosec A

2/x+y=1/cosec A

we know that 1/cosec A=sin A

2/x+y=sin A

(2/x+y)^2=sin^2 A----------(1)

subtract x and y

x=cosec A+cos A

y=cosec A-cos A

- - +

--------------------------

x-y=2cos A

x-y/2=cos A

(x-y/2)^2=cos^2 A-------------- (2)

(2/x+y)^2+(x-y/2)^2-1=0

sin^2 A+cos^2 A-1=0

we know that sin^2 A+cos^2 A=1

1-1=0

:-0=0