showing the equation is not an identity

[yasaminG]

in the expression square root (9-x^2), make the substitution x=3 sin @,and show that the result is 3Cos@

(@=theta)


the second problem is similar and i dont understand what to do either:

In the expression 1 / (u^2-25)^3/2 , make the substitution u = 5 sec @, and show that the result is cot^3@/125.

thank you.

 

[yasaminG]

anybody???!!

 

[stapel]

You haven't posted an equation, so there's nothing to solve.

Please reply with clarifications, including the instructions.

Thank you.

Eliz.

 

[yasaminG]

ok i edited it, sorry about that.

 

[stapel]

So the exercises are actually as follows:

. . . . .1) Let x = 3 sin(@), and show that the expression
. . . . ."sqrt[9 - x²]" may also be written as "3 cos(@)".

. . . . .2) Let u = 5 sec(@), and show that the expression
. . . . ."1/(u² - 25)^3/2)" may also be written as "cot³(@)/125".

When they say to "make a substitution", they mean to "plug this in for that". So, in (1), plug "3 sin(@)" in for "x" in "sqrt[9 - x²]":

. . . . .sqrt[9 - (3 sin(@))²] = sqrt[9 - 9sin²(@)]

...and so forth. Apply identities and algebra to rearrange into the desired expression.

Exercise (2) works the same way.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[yasaminG]

thank you, i wasnt squaring the nine so i kept getting a strange answer :!: