Please help me solve this identity problem cos²(x)-sin²(x)=0!! ?

Question

cos²(x)-sin²(x)=0

all i can think to do is make it cos²(x)=sin²(x) and i know thats not right... please help?

Thanks for the help!! :)

Answer 1

Also remember that cos²(x) + sin²(x) = 1

so cos²(x) = 1 - sin²(x)

and substituting into cos²(x)-sin²(x)=0

you get

1 - 2sin²(x) = 0

or 2sin²(x) = 1

take square root

sqrt(2) sin(x) = 1

sin(x) = sqrt(2)/2

x = 45 and 225, etc

Answer 2

cos²(x)-sin²(x)=0

cos²(x)=sin²(x)

sin²(x)/cos²(x) = 1

sin(x)/cos(x) = +/- 1

tan(x) = +/- 1

x = arctan (1) --->  x = 45 or 225 degrees (π/4 or 5π/4)

x = arctan(-1) --->  x = 135 or 315 degrees (3π/4 or 7π/4)

Answer 3

THis is not identity.

this is eqaution

x = 0 =>cos^2x - sin ^2 x = 1