Question

[Medal & Fan]
Prove the following identity:
sin4A + cos4A/1-2sin2A cos2A = 1

Answer 1

@mathmate

Answer 2

@.Sam.

Answer 3

sin4A + cos4A/1-2sin2A cos2A = 1

As is, mathematically actually means
\(sin4A + \frac{cos4A}{1}-2sin2A cos2A = 1\)

which is probably not what you mean.

So inserting parentheses will make it crystal clear:
\((sin4A + cos4A)/(1-2sin2A cos2A) = 1\)

or even better, use LaTeX
\(\Large \frac{\sin(4A) + \cos(4A)}{1-2\sin(2A) \cos(2A)} = 1 \)

You will notice that in LaTeX and in typeset documents, parentheses are not shown, BUT when transcribing to a single line, the parentheses are necessary.

Having said all that, the above cannot be proved, because it is not an identity. The value on the left-hand side varies with the angle A. When A equals 1 radian, the left-hand side evaluates to -0.8028, i.e. does not equal 1.

I suggest you double-check all mathematical expressions/equations before posting.

Answer 4

@mathmate Thanks for your response! And sorry, my bad. :/

Answer 5

hint: try
sum and difference formulas
product formulas
The following link is full of treasures for what you need to solve the problem:
http://www.regentsprep.org/regents/math/algtrig/att14/formulalesson.htm

Answer 6

@mathmate Thanks! I'll go through the site

Answer 7

@batmaaaanxD no problem!