Math, asked by basavarajab724, 16 days ago

27. If x= p tan 0 + q sec 0 and y= p sec 0 + q tan 0 then prove that x² - y2 = q2 -p2

Answers

Answered by manishaprajapati2222
0

Answer:

We have ,

L.H.S=

x

2

a

2

y

2

b

2

⇒L.H.S=

a

2

sin

2

θ

a

2

b

2

tan

2

θ

b

2

[∵x=asinθ,y=btanθ]

⇒L.H.S=

sin

2

θ

1

tan

2

θ

1

⇒L.H.S=cosec

2

θ−cot

2

θ [∵1+cot

2

θ=cosec

2

θ∴cosec

2

θ−cot

2

θ=1]

⇒ LHS =1= RHS

Hence, proved

Step-by-step explanation:

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Answered by amtkmr0
2

Answer:

True

Step-by-step explanation:

x² = p² tan²  + q² sec² + 2 pq tan . sec

y²  = p² sec²  + q² tan² + 2 pq tan . sec

x² + y²  = p² (tan² -sec² ) + q² (sec² -tan² )

            = p² (-1) + q² [ - (tan²  - sec² ) ]

            = - p² + q²  [ - (-1) ]

            = - p² + q²

= q²  - p² Proved.

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