Please help me to prove Sin^2 -Cos^2 =1 .....

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- anonymous

Please help me to prove Sin^2 -Cos^2 =1 .....

- jamiebookeater

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- anonymous

Sin^2(x)-Cos^2(x) does not equal one.

- anonymous

\[ \sin ^{2} - \cos ^{2} =1 \] Please Prove this....

- anonymous

\[\sin ^2(x)-\cos^2(x)\neq1\]

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## More answers

- anonymous

But I ve got this from a web site.... Here's the address.... Please go there and see whats wrong with it... .... http://www.cramster.com/practice-problems-p25-0-0-0-0-0-39167-0-cpi0-0.aspx

- anonymous

Which number?

- anonymous

In the Practice-3 Question set.... number 4

- anonymous

\[\sin ^2(x)+\cos^2(x)=1\]\[\sin ^2(x)-\cos^2(x)=-\cos(2x)\]

- anonymous

Oh.... Friutless can you please explain this farther......

- anonymous

Which one?

- anonymous

Your reply for the Question I 've asked.....

- anonymous

ok well this can be proved for sin(x)^2 + cos(x)^2 = 1 because this identity is true. you want to prove this?
THE IDENTITY sin(x)^2 - cos(x)^2 = 1 IS NOT TRUE. DON'T THINK ABOUT WHAT THE WEBSITE SAYS. IT IS NOT TRUE. PERIOD.
what would you like help proving?

- anonymous

It is asking which one from the choices is correct. It is obviously not D.

- anonymous

(i) is the correct answer.

- anonymous

Ok prove this one then... \[\sin ^{8}A-\cos ^{8}A = (\sin ^{2}A-\cos ^{2}A) (1- 2 \sin ^{2}A \cos ^{2}A)\]

- anonymous

apply the FOIL method to the right side (expand it)
\[-\cos^2(A)+\sin^2(A)+2 \cos^4(A) \sin^2(A)-2 Cos^2(A) Sin^4(A)\]

- anonymous

Replace the first two functions with an identity, and factor the rest.

- anonymous

Hmmmm.... friutless in which grade you're studying... ?

- anonymous

high school

- anonymous

In which country...?

- anonymous

usa

- anonymous

Really.... then I think you have done something similar to the syllbus of London A/L isn't you?

- anonymous

I am asking this from you because I am a student who has just started doing A/L s in Sri Lanka (somewhat similar to London A/L ). so I don't know the FOIL method.....
So I can't understand you're reply.....

- anonymous

Given (x-a)(y-b), applying FOIL yeilds xy-xb-ay+ab

- anonymous

Do the same on the trigonometric expressions

- anonymous

wow... I've got the right teacher here... thank you....

- anonymous

did you get the left side from this method?

- anonymous

\[Sin ^{8}A-\cos ^{8}A=( \sin ^{2}A-\cos ^{2}A)(\sin ^{6}A+\cos ^{6}A)+\sin ^{2}Acos ^{6}A-\cos ^{2}Asin ^{6}A\] Here's what I've done....... but I've stucked in it please try this also....

- anonymous

Please help me......

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