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Help!!!! Question is attached in photo-example-1
User Kirill Kay
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1 Answer

6 votes

ANSWER


\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

User Arminda
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