Question

Thank You for taking the time to look at this.

If x = 2cos^2(theta) and y = sin2(theta), show that (x -1)^2 + y^2=1

Answer 1

I tried my best but I couldn't solve this! Where did you get this question from?

Answer 2

substitute:
(2cos^2(theta)-1)^2 + (sin2(theta))^2 = 1

then recall some identities:
*2cos^2(theta)-1=cos2(theta)
*cos2(theta)=cos^2(theta)-sin^2(theta)
*sin^2(theta)=1-cos^2(theta)

therefore, it will become:
(cos2(theta))^2 + (sin2(theta))^2=1
>>actually, here you can conclude they are equal because of the identity:
cos^2(theta) + sin^2(theta) = 1
anyway, continuing and substituting the 3rd identity to the equation,,
(cos2(theta))^2 + 1-(cos2(theta))^2 = 1
therefore, the cosines will cancel each other, leaving 1,,

i hope i was able to help.. =)