Question

If x = p sec θ + q tan θ and y = p tan θ + q sec θ, then prove that x2 – y2 = p2 – q2

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x²-y²=p²+q²

Step-by-step explanation:

here given x= p secθ +qtanθ

y=ptanθ +q secθ

if we substitute x and y in equation x²-y²

x²-y²=(p secθ +qtanθ)²- (ptanθ +q secθ)²

=[(p sec θ )²+(qtan θ )²+2 pq sec θ tan θ ] - [(p tan θ)²+(qsec θ )²+2pq sec θ tan θ ]

=p² sec² θ + q²tan² θ + 2pq sec θ tan θ - p² tan² θ -q²sec² θ -2pq sec θ  tan θ 

= p² sec² θ +q²tan² θ -p²tan² θ -q²sec² θ 

=p²(sec² θ -tan² θ ) + q²(sec² θ -tan² θ ) =p²+q²

here we know sec² θ -tan² θ =1

therefore. x²-y²=p²+q²

hence proved