p180 ex8b q5
prove the following identities:
Hello, afeasfaerw23231233!
Your textbook has an error.
. . Incredibly, it produces the desired result!
Let
Then we have: . . . . . This is not correct!
Do you know the basis for this strange substitution?
In case you don't, I'll explain it.
We let: .
So we have: .
That is, angle is in a right triangle with:
. . Using Pythagorus, we have: .
Then: .
We also have: .
and: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Back to the problem . . .
We have: .
Substitute: . . . Your book left out the radicals.
Multiply top and bottom by
. .
Factor and reduce: .
Therefore, we have: . . . . . There!