Help with Identities!?

Question

Prove Identities:
1. cos(theta)=1-2sin^2(theta)
2. sec(a-b)=(seca*secb)/(1+tana*tanb)

Please help me with these problems if you understand how to work them. Thanks

sorry the 1st question is actually:
cos(2*theta)= 1-2sin(^2)theta

Answer 1

1) cos(t) = 1 - 2sin^2(t) This is false.

Let t = -pi/2.
cos(-pi/2) = 0
1 - 2sin^2(-pi/2) = 1 - 2[-1]^2 = 1 - 2 = -1
0 is not equal to -1.

Answer 2

1. If theta is 90 degrees ( or pi/2 radians) then cos(theta) = 0, but 1-2sin^2(theta) = 1 - 2*(1^2) = -1

Not equal.

2.
If a = b and 0 < b < 45 degrees
then

sec(a-b) = 1

0 < sec(a)*sec(b) < 1
1 < 1+tana*tanb < 2

Therefore
(seca*secb)/(1+tana*tanb) < 1
not equal to sec(a-b) = 1

Answer 3

The first identity is not true as written; I think you left out a 2 somewhere. Probably to prove it you need to apply the general formula for cos(theta + phi).
The second formula did not come out; you need to add a space somewhere or Yahoo Answers won't display it properly.

Answer 4

try to check the identities again, write it clearly.