Verify the identity: sin(a+b)/tana+tanb=cosacosb

Question

 Verify the identity.

Answer 1

Hi Jasmine,

 

Try replacing sin(a+b) with sina cosb + cosa sinb.

 

Replace tana with sina/cosa.

 

Replace tanb with sinb/cosb.

 

Now you have a complex fraction. There are a couple ways to go from there. 

 

I like to multiply numerator and denominator of the "big" fraction by the LCD of the "little" denominators (cosa cosb).

 

The results for the new numerator will be: cosacosb (sinacosb+cosasinb)

 

The results for the new denominator will be: (sinacosb+cosasinb)

 

The common factor that appears in the new numerator and denominator can be cancelled leaving cosacosb. QED

 

You can also simplify the complex fraction by combining the two fractions in the denominator to one fraction, then multiply the numerator by the reciprocal of the denominator.