Question

If sin + cosec = 2 then show that sin⁷ + cosec⁷ =?​

Answer 1

Step-by-step explanation:

Explanation:

Solving

sin

x

+

1

sin

x

=

2

→

sin

2

x

−

2

sin

x

+

1

=

0

we have

sin

x

=

1

then

sin

n

x

+

1

sin

n

x

=

2

This can be also demonstrated by finite induction.

1) First it is true for

n

=

1

(with sin x = 1 of course)

2) Supposing that it is true for

n

then

3) Prove that it is true for

n

+

1