Question Below, True or False?

For all values for which the expressions are defined, sin x - cos x and





_____1_____ are equivalent expressions.


sin x + cos xQuestion Below, True or False?
no.





take x = 45 degrees


then sin x - cos x = 0


while 1/(sinx + cosx) %26gt; 0





i think i understan a bit how you can get so far


(sin x - cos x ) * (sin x + cos x) = sin ^2x MINUS cos^2x


and 1 = sin^2 x PLUS cos ^ 2 xQuestion Below, True or False?
Let's see: sin(x) is an odd function, so sin(-x) = - sin(x)


and cos(x) is an even function, so cos(-x)= cos(x)





Note that sin(x) and cos(x) are defined on [0,2pi]





so, sin(x) - cos(x) = sin(x) - cos(-x) are equivalent.





Not sure the meaning of sin(x) +cos(x)...if this is your answer, it is incorrect.
To answer this question, simplt set the two expressions equal to each other. Play with the algebra, and if you eventually get something you know is false (like 2=1), then you know your premise (that they are equal) is false.





The contradiction is not hard to find. (sin+cos)(sin-cos)=sin^2-cos^2=1? Not true, except when sin= +/-1 and cos = 0 (x=pi/2 +k*pi, where k is an integer). Also, sin + cos is never equal to 0, so you don't even need to worry about things being defined, since you never divide by zero.
true
ok there are a few rules when doing this well not rules but stuff like sin^2x + cos^2x = 1 so really with the 1/sin x + cos x well I know they do equal its to hard to explain using this website