Which of the following is an identity?

A. cosx(2sinx+1)=0
B. sin^2x=4-2cos^2x
C. (tanx+cotx)(sinx*cosx)=1
D. secx*tanx-cosx*cotx=sinx

Question

Which of the following is an identity?

A. cosx(2sinx+1)=0
B. sin^2x=4-2cos^2x
C. (tanx+cotx)(sinx*cosx)=1
D. secx*tanx-cosx*cotx=sinx

anonymous · Answer

An identity is true for any value of the variable.
Did you try simplifying the above?

anonymous · Answer

Yes I know its not A...

anonymous · Answer

ok, Since sin^2(x)+cos^2(x) = 1 and the range of cos is [-1,1] can B be correct?

anonymous · Answer

I get for B: cos^2 (x) + sin^2 (x) =2. I did not end up with 1.

anonymous · Answer

So, B's wrong. Now check  C, by writing tan x = sin x /cos x and cot x = cos x / sin x.
Also use the above identity once again.

anonymous · Answer

I think C is the right answer

anonymous · Answer

Yes. And did you check D?

anonymous · Answer

no.....

anonymous · Answer

There is an easier way to check for identities. Put a value for 'x'(say 0,90..) and check whether you get a true equation. Remember that it may not always work out.