QUESTION 5 DO NOT USE A CALCULATOR FOR THIS QUESTION. 5.1 Complete the following identities: 5.1.1 $$ \quad \cos ^{2} \mathrm{~A}+\sin ^{2} \mathrm{~A}=\ldots $$ $$ 5.1 .2 \quad \cos ^{2} \mathrm{~A}-\sin ^{2} \mathrm{~A}=\ldots $$

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### 5.1.1

We start with the Pythagorean Identity:

$$
\cos^2 A + \sin^2 A = 1
$$

### 5.1.2

Recall the double-angle formula for cosine:

$$
\cos 2A = \cos^2 A - \sin^2 A
$$

Thus,

$$
\cos^2 A - \sin^2 A = \cos 2A
$$
5.1.1 $$ \cos^{2} A + \sin^{2} A = 1 $$ 5.1.2 $$ \cos^{2} A - \sin^{2} A = \cos 2A $$

QUESTION 5
DO NOT USE A CALCULATOR FOR THIS QUESTION.
5.1 Complete the following identities:
5.1.1

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5.1.1

5.1.2

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