Question

trig identities : check

Answer 1

i believe this is false but im not sure

Answer 2

Square both sides?

Answer 3

is that allowed?

Answer 4

i think it's false

Answer 5

I think you get something like \[\cos^2 \frac{ a }{ 2 } = \frac{ 1-\cos(a) }{ 2 }\]

Answer 6

thats what i did

Answer 7

You either want to prove it's true, or find a counter example. Maybe try some easy values to see if you can get one that doesnt work?

Answer 8

Try a=0

Answer 9

Is the way I did it correct? By squaring both sides?

Answer 10

for questions like this maybe its best to plug it in?

Answer 11

Or a=pi

Answer 12

so it's false

Answer 13

Plugging in values will only work to DISprove an identity, e.g., show it's NOT an identity. That's fine as a way to disprove it. Just don't ever try it to PROVE it, there you must show that it works for ALL values of the variable so you have to show it algebraically. :)

Answer 14

alright!

Answer 15

Yup, it's false - you see that it doesn't work for a=0 or a=pi. If you've studied half-angle identities, you'll see that the RHS is actually =sin(a/2)

Answer 16

ah i see thanks!