Exact values of expressions and establishing identities

[Violagirl]

Hi I was wondering if someone could show me how to set up these two problems:

Find the exact value of each expression.

1. sec(tan^-1 1/2)

2. cot(sin^-1 (-sq.rt. 2/3)

And then how would you do this one?

Establish the identity:

sec u-tan u= cosu/1+sin u

Any help would be great!

 

[Deleted member 4993]

Hi I was wondering if someone could show me how to set up these two problems:

Find the exact value of each expression.

1. sec(tan^-1 1/2)

2. cot(sin^-1 (-sq.rt. 2/3)

And then how would you do this one?

Establish the identity:

sec u-tan u= cosu/1+sin u

Any help would be great!

(1) let

\(\displaystyle \tan^{-1}[\frac{1}{2}] \, = \, \theta\)

you need to find

\(\displaystyle \sec(\theta) \, = \, ??\)

\(\displaystyle \tan(\theta) \, = \, \frac{1}{2}\)

\(\displaystyle \tan^2(\theta) \, = \, \frac{1}{4}\)

Now continue....

Please show your work, indicating exactly where you are stuck - so that we know where to begin to help you.