Prove by mathematical induction that where sinθ≠0 for all positive integers n.

For , on the left we have , and on the right,

(where we use the double angle identity: )

Suppose the relation holds for :

Then for , the left side is

So we want to show that

On the left side, we can combine the fractions:

Recall that

so that we can write

(another double angle identity: )

Then recall that

which lets us consolidate the numerator to get what we wanted:

and the identity is established.

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>