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If x = 2cos^2(theta) and y = sin2(theta), show that (x -1)^2 + y^2=1
If x = 2cos^2(theta) and y = sin2(theta), show that (x -1)^2 + y^2=1
Answers
Answered by
Aishwarya
I tried my best but I couldn't solve this! Where did you get this question from?
Answered by
jai
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.. =)
(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.. =)
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