ABCof calculus is come under calculus-1 category and it deals with pre-calculus problems. So the term pre-calculus is referred as ABC of calculus in which it deals with secondary algebra problems. Pre-calculusis the combined version of secondary algebra and trigonometry. Basically ABC of calculus deals with solving algebra and trigonometry problems. It prepares the students for learning algebra-1 problems and it is also referred as introduction to analysis. The following are example problems which explain the concept of ABC of calculus.

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**Example 1:**

Solve trigonometric expression.

[Sin ^{4}x - cos ^{4}x] / [sin ^{2}x - cos ^{2}x]

**Solution:**

Factor the numerator term

[sin ^{4}x - cos ^{4}x] / [sin ^{2}x - cos ^{2}x]

= [sin ^{2}x - cos ^{2}x][sin ^{2}x + cos ^{2}x] / [sin ^{2}x - cos ^{2}x]

Solve it

= [sin ^{2}x + cos ^{2}x]

**[Sin ^{4}x - cos ^{4}x] / [sin ^{2}x - cos ^{2}x] = 1 **

**Example 2:**

Solve the trigonometric expression.

sin ^{2}x - cos ^{2}x sin ^{2}x

**Solution:**

Factor sin ^{2}x out, group and simplify

sin ^{2}x - cos ^{2}x sin ^{2}x

= sin ^{2}x (1 - cos ^{2}x) **sin ^{2}x - cos ^{2}x sin ^{2}x**

**Example 3:**

Determine s(4), t(4) and s(4) / t(4) where functions s and t are defined by

s (y) = 3y - 8 , t (y) = y^{ 2} - 16

**Solution:**

Evaluate s(4)

s(4) = 3(4) - 8 = 4

Evaluate t(4)

t (4) = 4 ^{2} - 16

= 16 -16 = 0

While calculating s (4) / t(4), t(4) in which the denominator is equal to 0.

**s (4) / t (4) = undefined **

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1) Solve trigonometric expression.

[Sin ^{2}x - cos ^{2}x] / [sin ^{4}x - cos ^{4}x]

**Answer: 1 / [sin ^{2}x + cos ^{2}x] = 1**

2) Determine, s (4), t (4) and s (4) / t (4) where functions s and t are defined by

s (y) = 4y - 6 , t (y) = y^{ 2} - 25

**Answer: s (4) / t (4) = -10/9**