Question

79. If x = a sin 0 and y = b tan 0, prove that a²y²-b²x² = x²y²
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Answer 1

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