Question

x = cotΘ + cosΘ , y = cotΘ − cosΘ, prove that, x² − y² = 4√xy .

Answer 1

Answer:

sinθ

cosθ

+

cosθ

sinθ

=x

⇒

sinθcosθ

1

=x

y=

cosθ

1

−cosθ=

cosθ

1−cos

2

θ

=

cosθ

sin

2

θ

x

2

y=

cosθ

sin

2

θ

×

sin

2

θcos

2

θ

1

=

cos

3

θ

1

xy

2

=

sinθcosθ

1

×

cos

2

θ

sin

4

θ

=

cos

3

θ

sin

3

θ

⇒(x

2

y)

2/3

−(xy

2

)

2/3

=

cos

2

θ

1

−

cos

2

θ

sin

2

θ

=1.