Question

if sin2 theta=k, then the value of tan^3theta/1+tan^2theta+cot^3/1+cot^2theta=​

Answer 1

Step-by-step explanation:

We have,

sinθ=k,

Since,

1+tan

2

θ

tan

3

θ

+

1+cot

2

θ

cot

3

θ

=

sec

2

θ

tan

3

θ

+

csc

2

θ

cot

3

θ

=

cos

2

θ

1

cos

3

θ

sin

3

θ

+

sin

2

θ

1

sin

3

θ

cos

3

θ

=

cosθ

sin

3

θ

+

sinθ

cos

3

θ

=sinθcosθ(sin

2

θ+cos

2

θ)

=sinθcosθ

=

k

2

−1

k