Prove that Cot 4x (sin 5 x + sin 3 x) = Cot x (sin 5 x - sin 3 x) ?
2 Answers
Right side:
Left side:
They're equal
Factor formula (Sum-to-Product and Product-to-Sum identities)
Explanation:
For this question, we can use the Sum-to-Product and Product-to-Sum identities.
I'm lazy, so here's a picture of the identities.
The product-to-sum formula above can be derived via compound angle identities.
Using the substitution
So, now that we've got that sorted out, let's apply our formulas.
Alternatively, you could also apply the sum-to-product formula on the right-hand side: