Question

I need help finding the exact value of cos^2pi/8-sin^2pi/8

Answer 1

use the identity,
$$\cos (2x)=\cos^2(x)-\sin^2(x)$$

Answer 2

Simplify the following:
(cos(pi))^2/8-sin(pi)^2/8
Evaluate cos(pi)^2.
cos(pi)^2 = 1:
1/8-sin(pi)^2/8
Evaluate sin(pi)^2.
sin(pi)^2 = 0:
1/8-0/8
Any number times zero is zero.
0/8 = 0:
1/8
Look for the additive identity.
1/8+0 = 1/8:
Answer: 1/8

Answer 3

Sorry I wrote the problem wrong its actually
cos^2(pi/8)-sin^2(pi/8)

Answer 4

Still you can use the above identity to find the answer

Answer 5

Can you give me the first step please I'm still lost

Answer 6

okaii so these are the steps for the problem: cos^2pi/8-sin^2pi/8
you can you the same methods and steps(similar) to do the other one you want to do? any questions or doubts you still have please post them :)

Answer 7

@some_someone
jinxed401 is mentioning about
$$\cos^2(\pi/8)-\sin^2(\pi/8)$$ not
$$\frac{\cos^2(\pi)}{8}-\frac{\sin^2(\pi)}{8}$$

@jinxed401
As i said, consider the identity,
$$\cos(2x)=\cos^2(x)-\sin^2(x)$$
if you substitute x=pi/8 what would the above equation be?

Answer 8

\[\cos(2\times \pi/8 ) =\cos^2(\pi/8)-\sin^2(\pi/8)\] I"m still not sure where to go here

Answer 9

the finally it can be cos(2pi/8) = cos(pi/4) = cos45 degrees = ... ?

Answer 10

45 degrees was the special angle in trigono.. u have to memorize the values of sin, cos, tan for the special angles

Answer 11

cos45 is \[(\sqrt{2}/2)\]

Answer 12

yes, that;s right

Answer 13

but I'm not seeing where you got 45 degrees from though
because (pi/8) is does not come out to be (pi/4)

Answer 14

2/8 = 1/4 and
1 pi radian = 180 degrees
so, 1/4 pi = 1/4 * 180 degrees = 45 degrees

Answer 15

it just converting unit radian to degree

Answer 16

Yes but where are you getting (1pi/8)

Answer 17

hoho... ur original problem is cos^2pi/8-sin^2pi/8
so, we change this by identity what our friend said above ^
thus, cos^2pi/8-sin^2pi/8 = cos(2pi/4)
just doing for right side, dont look for left side because it has passed away :)

Answer 18

you are an amazing person

Answer 19

i just continue it :)