If sinθ+cscθ=5, then the value of sin
3
θ+csc
3
θ is:

Let x=sinθ. Since cscθ=
sinθ
1
​
, we can write cscθ=
x
1
​
.
The given equation is:

x+
x
1
​
=5
We need to find the value of sin
3
θ+csc
3
θ=x
3
+
x
3

1
​
.

Using the algebraic identity:

(x+
x
1
​
)
3
=x
3
+
x
3

1
​
+3(x+
x
1
​
)
Substitute the value x+
x
1
​
=5:

5
3
=x
3
+
x
3

1
​
+3(5)
125=x
3
+
x
3

1
​
+15
x
3
+
x
3

1
​
=125−15=110