Trigo “Product to Sum” formula

Trigo “Sum to Product” formula is given in the math formula list MF26. However,  “Product to Sum” formula is not in the formula list. Yet, students are often required to use the “Product to Sum” formula in mathematical induction or integration. Hence, knowing how to derive the “Product to Sum” formula from “Sum to Product” formula is critical.

“Sum to Product” formula

sum or factor formula

To derive the “Product to Sum” formula

Let P = X+Y and Q= X-Y

Substitute into the “Sum to Product” formula, we derived the “Product to Sum” formula

product

Try out this question

2011 P1, 6iii

capture

Partial fraction: Cover-up rule

Partial fraction is commonly used in binomial expansion, method of difference and integration.

When the divisor consists only of linear factors, cover up rule can be used to find the constants in the partial fraction quickly.

Example

Express Tex2Img_1400545440 in partial fraction.

Tex2Img_1400545549

By cover up rule,

1

Therefore

Tex2Img_1400546214

2

0 = A+C

3

Therefore,

fraction final

 

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