Question

x=cot theta+tan theta y=sec theta-cos theta then (x^2y) ^2/3-(xy^2) ^2/3=​

Answer 1

Answer:

The question should be:

prove that (x

2

y)

3

2

−(xy

2

)

3

2

=1

cotθ+tanθ=

tanθ

1+tan

2

θ

=

tanθ

sec

2

θ

⇒x=cotθ+tanθ=

sinθcosθ

1

secθ−cosθ=

cosθ

1cos

2

θ

=

cosθ

sin

2

θ

⇒y=secθ−cosθ=

cosθ

sin

2

θ

∴x

2

=

sin

2

θcos

2

θ

1

,y

2

=

cos

2

θ

sin

4

θ

∴x

2

y=

sin

2

θcos

2

θ

1

×

cosθ

sin

2

θ

=sec

3

θ

∴xy

2

=

sinθcosθ

1

×

cos

2

θ

sin

4

θ

=tan

3

θ

∴(x

2

y)

3

2

−(xy

2

)

3

2

=(sec

3

θ)

3

2

−(tan

3

θ)

3

2

=sec

2

θ−tan

2

θ

=1