Step-by-step explanation:
9. sin ((n−1) A) sin ((n+1) A) + cos ((n−1) A) cos ((n+1) A)
From angle difference formula, we know that:
cos (α − β) = sin α sin β + cos α cos β
Therefore, we can rewrite this as:
cos ((n−1) A − (n+1) A)
cos (nA − A − nA − A)
cos (-2A)
Using reflection property:
cos (2A)
10. sin ((n−2) A) cos (nA) − cos ((n − 2) A) sin (nA)
From angle difference formula, we know that:
sin (α − β) = sin α cos β − cos α sin β
Therefore, we can rewrite this as:
sin ((n−2) A − nA)
sin (nA − 2A − nA)
sin (-2A)
Using reflection property:
-sin (2A)
