perplexus.info :: Just Math : Radical difference trigonometry

Radical difference trigonometry (Posted on 2023-04-16)

Simplify the expression:

√[sin⁴x+4cos²x] - √[cos⁴x+4sin²x]

Source: AMC12 2002

See The Solution Submitted by Jer

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re: simplified / two wrongs made a right?

| Comment 2 of 3 |

(In reply to simplified by Larry)

The reason I shared this problem is that it has a very subtle trap.

I won't correct it right away, but it's in the upper part. [The first wrong]

The final answer is cos(2x) but that isn't the correct simplification for (sin(x))^2 - (cos(x))^2 which would be -cos(2x) [the second wrong.]

Posted by Jer on 2023-04-18 09:29:15

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