Question

please solve Q no. 16 fastly . It is very important

Answer 1

bhai no one is here who. can answer this
i am telling you the truth

Answer 2

let
L1 = xcosø - ysinø - kcosø
L2 = xsecø + ycosecø - k

by using the formula to find the distance between a line and a point
and the formula is
|Ax1 + By1 + C|÷ √(A^2 +B^2)

distance from origin to L1 = p = kcos2ø
distance from origin to L2 = q =
k/√(sec^2ø + cosec^2ø)

now,

p^2 = k^2cos^2(2ø)
4q^2 = 4k^2/sec^2ø + cosec^2ø

Now take L.H.S

p^2 + 4q^2

k^2cos^2(2ø) + 4k^2/sec^2ø + cosec^2ø

k^2{(cos^2ø -sin^2ø) - 4/(1÷cos^2ø) + (1÷sin^2ø)}

By taking LCM and multiply we have

k^2{cos^4ø + sin^4ø - 2cos^2øsin^2ø + 4sin^2øcos^2ø)

k^2{cos^4ø + sin^4ø + 2sin^2øcos^2ø}

k^2(cos^2ø + sin^2ø)^2

k^2
hence proved. :-)