trig identities: sin^2(x) + cos^2(x) = 1, sin(2x) = ....

[Guest]

How do I prove these identities?

. . .a) sin²(x) + cos²(x) = 1 (use C and cos(0) = 1)

. . .b) sin(2x) = 2sin(x)cos(x)

. . .c) cos(2x) = 2cos²(x) - 1

I'm supposed to use these identities:

. . .A) sin(-x) = -sin(x)
. . .B) cos(-x) = cos(x)
. . .C) cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
. . .D) sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

Thanks in advance for your help!

 

[tkhunny]

Hint on b) and c)

cos(2x) = cos(x + x)

 

[stapel]

There is no plug-n-chug "formula" for proving identities, and there will often be many ways of proving the same identity. You need to try various substitutions and see what you can accomplish.

So, following the tutor's hints, what have you gotten? Please show all of your steps. Thank you.

Eliz.