Question

If x=psecalphacosbeta y=qsecalphasinbeta and z=rtanalpha then show that
x²/p²+y²/q²-z²/r²= 1​

Answer 1

Step-by-step explanation:

x=p sec α cos β

y=q sec α sin β

z= r tanα

now, x= p secα cosβ

or, sec α sin β = x/p

or, sec²α cos² β= x²/p²

similarly ,y= q secα sin β

or, sec α sin β = y/q

or, sec²α sin² β= y²/q²

z= r tan α

or, tan α=z/r

or,tan²α=z²/ r²

so, x²/p²+ y²/q² -z²/ r²

= sec²α cos²β + sec²α sin²β -tan² α

= sec²α( sin²β +cos²β) - tan²α

= sec²α - tan² α= 1 (proved)

hope u got the answer!