Question

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Answer 1

`\tan( \alpha ) + \tan( \beta )`

Step-by-step explanation

The given identity is

`( \sin( \alpha + \beta ) )/( \cos( \alpha ) \cos( \beta ) )`

We expand the numerator to get:

`= ( \sin\alpha \cos\beta + \sin\beta \cos \alpha )/( \cos( \alpha ) \cos( \beta ) )`

Split the numerator to obtain:

`= ( \sin\alpha \cos\beta )/( \cos( \alpha ) \cos( \beta ) ) + ( \sin\beta \cos \alpha )/( \cos( \alpha ) \cos( \beta ) )`

Cancel the common factors:

`= ( \sin\alpha )/( \cos( \alpha ) ) + ( \sin\beta )/( \cos( \beta ) )`

This simplifies to give us;

`= \tan( \alpha ) + \tan( \beta )`

The second choice is correct