Question

If x=p tan o +q sec o and y=p sec o + q tan o then prove that X2 -y2=q2-p2​

Answer 1

Step-by-step explanation:

x = p tanO+q secO

y= p secO+ q tanO

x² = ( p tanO+q secO)²

y² = ( p secO+ q tanO)²

x² = p² tan²O+q²sec²O + 2pqtanOsecO

y² = p²sec²O+q² tan²O + 2pqtanOsecO

-___-______-_______-_____________

x²-y² =p²(tan²O-sec²O) +q²(sec²O-tan²O)

x²-y² =p²( -1 ) +q²( 1 )

x²-y² = - p²+q²

x²-y² = q²- p²

Hope the solution is clear...