Question

18.
Eliminate from the equations :
a cot 0 + b cosec 0 = x2, b cot 0 + a cosec 0 = y2​

Answer 1

Solution :

The given equations are

a cotø + b cosecø x² ............(1)

and b cotø +a cosecø y² ..(2)

Squaring and subtracting (1) and (2), we have

=> a²cot² ø + b²cosec²ø + 2a b cotø cosecø

=> -(b² cot² ø +a² cosec² ø + 2 a b cotø cosec ø) =x^4 - y^4

=> -a²(cosec²ø -cot²ø) +b² (cosec²ø -cot²ø) x^4 - y^4

=> -a² +b² = x^4 - y^4

=> i.e. b²-a² = x^4 -y^4, which is the required eliminant.