Home
Class 12
MATHS
The equation sec ^2 theta = ( 4xy )/...

The equation ` sec ^2 theta = ( 4xy )/( ( x+y)^2)` is possible for x,y, ` in R ` only if

A

`x = y ne 0 `

B

`x = y,x ne 0`

C

`x = y`

D

`x ne 0, y ne 0`

Text Solution

Verified by Experts

The correct Answer is:
(a,b)
We know that, ` sec ^(2) theta ge 1 `
` rArr " " ( 4xy )/((x + y ) ^(2)) ge 1 `
` rArr " " 4xy ge (x + y ) ^(2)`
` rArr ( x + y) ^(2) - 4xy le k 0 `
` rArr " " (x - y )^(2) le 0 `
` rArr x - y = 0 `
` rArr " " x = y `
Therefore, ` x + y = 2x " " ` [add x both sides]
But ` x + y ne 0 ` since it lies in the denominator,
`rArr 2x ne 0 `
`rArr x ne 0 `
Hence, ` x = y , x ne 0 ` is the answer.
Therefore, (a) and (b) are the answers.
Promotional Banner

Similar Questions

Explore conceptually related problems

sin theta = ( x + Y)/( 2 sqrt(xy)) is possible

The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

sec^2theta=(4x y)/((x+y)^2) is true if and only if x+y!=0 (b) x=y ,x!=0 x=y (d) x!=0,y!=0

(x+y)(x^(2)- xy +y^(2)) is equal to

Verify the differential equation y = x sin x : xy' = y + x sqrt(x^(2) - y^(2))(x ne 0 and x gt y or x lt -y)

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

The HCF of x^(2) - 2xy + y^(2) and x^(4) - y^(4) is ……… .