Trig Help!

[jhunt47]

I need help with the some math problems. they are really really hard, and I want to know how to do them (not for homework, but for an upcoming test that the teacher said they would be on!).

Prove the following identity:
#1
(tanx + cotx)/(secx - tanx) = sec^2x-(secx)(tanx)
The teacher already told us that it would be an identity, but we have to be able to prove why without using other known identities.

Solve the following equations:
#1
1-2sin^2(2x) = 3sin(2x)

#2
(16/81)^(sin^2(x)) + (16/81)^(1-sin^2(x)) = 26/27

I am not sure how to even start this second one, and I am really nervous! Any help is greatly appreciated!!!!

 

[Deleted member 4993]

I need help with the some math problems. they are really really hard, and I want to know how to do them (not for homework, but for an upcoming test that the teacher said they would be on!).

Prove the following identity:
#1
(tanx + cotx)/(secx - tanx) = sec^2x-(secx)(tanx)
The teacher already told us that it would be an identity, but we have to be able to prove why without using other known identities.


You cannot prove these without using some identity - which one you are not allowed to use?

Solve the following equations:
#1
1-2sin^2(2x) = 3sin(2x)

The left-hand-side is a "famous" double-angle expression.

#2
(16/81)^(sin^2(x)) + (16/81)^(1-sin^2(x)) = 26/27

\(\displaystyle \left [ \frac{16}{81}\right ]^{sin^2x} + \frac{\frac{16}{81}}{\left [ \frac{16}{81}\right ]^{sin^2x}} = \frac{26}{27}\)

substitute:

\(\displaystyle u = \left [ \frac{16}{81}\right ]^{sin^2x}\)

and continue.....


I am not sure how to even start this second one, and I am really nervous! Any help is greatly appreciated!!!!