Trignometry

[l9876]

Hi Everyone,
Can you help me solve the following :

1) Tan (Cos^-1 8/17)
2) Cos (Sin^-13/5 + Sin^-1 5/13)
3) Sec^2(tan^-12) + Cosec^2 (Cot^-1 3) =15

 

[Deleted member 4993]

Hi Everyone,
Can you help me solve the following :

1) Tan (Cos^-1 8/17)
2) Cos (Sin^-13/5 + Sin^-1 5/13)
3) Sec^2(tan^-12) + Cosec^2 (Cot^-1 3) =15

Yes we can help - if you can show us your work and tell us exactly where you are stuck.

We will start you off in the first one:

\(\displaystyle \cos^{-1}(x) \ \ = \ \ \theta\)

\(\displaystyle \cos(\theta) \ \ = \ \ x\)

\(\displaystyle \tan(\theta) \ \ = \ \ \pm \frac{\sqrt{1-x^2}}{x}\)

\(\displaystyle \tan(\cos^{-1}(x)) \ \ = \ \ \pm \frac{\sqrt{1-x^2}}{x}\)