Trig Identities

[ds197]

Hi,:smile:


So I was given a problem : tanϴ + 1/tanϴ = 1/sinϴcosϴ

Since the L.S has to = to the R.S, I started with the left side (most complicated) and have sinϴ/cosϴ for the tanϴ(since tanϴ= sinϴ/cosϴ).
But I don't know what to do for the 1/tanϴ....


Thank you for your help!

 

[Deleted member 4993]

Hi,:smile:


So I was given a problem : tanϴ + 1/tanϴ = 1/(sinϴcosϴ)

Those () are important - without those it is not an identity

Since the L.S has to = to the R.S, I started with the left side (most complicated) and have sinϴ/cosϴ for the tanϴ(since tanϴ= sinϴ/cosϴ).
But I don't know what to do for the 1/tanϴ....


Thank you for your help!

Fundamental rule of algebra:

\(\displaystyle \dfrac{c}{\left (\frac{a}{b}\right )} \ = \ c * \dfrac{b}{a}\)

so

\(\displaystyle \dfrac{1}{tan(\theta)} \ = \ \dfrac{1}{\frac{sin(\theta)}{cos(\theta)}} \ = \ 1 * \dfrac{cos(\theta)}{sin(\theta)} \ = \ \dfrac{cos(\theta)}{sin(\theta)}\)