Trigonometric Proofs

[GeTDaBooTaYShaKn]

1+ cot[/u = cot
1+ tan

Can anyone help me prove that they equal each other and are an identity?? Thanks so much!

 

[Aladdin]

Correct . . . Mission Accomplished

 

[Deleted member 4993]

1+ cot[/u = cot
1+ tan

Can anyone help me prove that they equal each other and are an identity?? Thanks so much!

Another way:

\(\displaystyle \frac{1 + cot(\theta)}{1 + tan(\theta)} \, = \, \frac{1 + cot(\theta)}{1 + \frac{1}{cot(\theta)}} \, = \,\frac{cot(\theta)\cdot [1 + cot(\theta)]}{1 + cot(\theta)} \, = \, cot(\theta)\)

 

[GeTDaBooTaYShaKn]

Thanks so much! You're right... the second way was much easier lol.