Question

Simplify (sin^2)*(67.5deg) - (cos^2)*(67.5deg) and then evaluate exactly.

Answer 1

well, cos 2x = cos^2 x - sin^2 x, so what do you think?

If you end up with 1/√2 you are correct.

Answer 2

How exactly do you get there though? I tried to follow a similar homework problem and got:

= (cos^2)*(67.5deg) - (sin^2)*(67.5deg)
= cos(2*67.5deg)
= cos135deg
= -√2/2

Answer 3

note that the problem was

sin^2(67.5)-cos^2(67.5)
= -cos(135)

my hint was not intended to make you forget what was originally asked. :-)

And, I know lots of folks hate roots in the denominator, but I see no reason why √2/2 is better than 1/√2. Just mt preference

Answer 4

Thank you very much!