Ratios of operations with angles

- Ratios of the addition of angles:

· sin (α + β) = sinα·cosβ + cosα·sinβ

· cos (α + β) = cosα·cosβ - sinα·sinβ

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Example: 

- Ratios of the subtraction of angles:

· sin (α - β) = sinα·cosβ - cosα·sinβ

· cos (α - β) = cosα·cosβ + sinα·sinβ

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Example:

- Ratios of the double angle:

· sin (2α) = 2sinα·cosα

· cos (2α) = cos²α - sin²α

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Example: 

- Ratios of the half angle:

 

Example: 

 

 

Exercises:

1.- Calculate by using the formulas:

a) tan 75^o

b) cos 15^o

c) sin 90^o    (by using 90^o = 2·45^o)

 

2.- Check these identities:

Solutions: a) 2 + √3; b) (√6+√2)/4; c) 1