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How do I verify an identity? The problem is:

tan2(theta) + cot2(theta) / sec2(theta) = csc2(theta)

2007-11-26 08:10:54 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

This is not an identity. The proof is easy. Just calculate it for any angle and find that it is not true.
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2007-11-26 08:43:53 · answer #1 · answered by oregfiu 7 · 0 0

tan2(theta) + cot2(theta) / sec2(theta) = csc2(theta)
tan(2x) + cot(2x) / sec(2x) = csc(2x)

tan (2x) = 2 tan / 1-tan^2

cot (2x) = 1- tan^2 / 2 tan

sec(2x) = 1/ cos(2x) =

csc (2x) = 1/ sin(2x) = 1/(2sincos)

(2tan/1-tan^2) + (1-tan^2/2tan) / sec(2x)

[4 tan^2 + (1-tan^2) ^2 ] / tan(1-tan^2) *cos(2x)

4 tan^2 + (1-tan^2) ^2 = 4 tan^2 + 1 - 2tan^2 + tan^4
1 - 2tan^2 + tan^4 = (tan^2 - 1)^2

so the numerator is:
tan^2 - 1
------------
tan(1-tan^2) *cos(2x)

tan^2 - 1
------------
-tan(tan^2 -1) *cos(2x)

-1 / tan * cos(2x)

(cos^2 - sin^2)tan = -1/(cos - sin^3/cos)

i don't know...

2007-11-26 16:27:06 · answer #2 · answered by sayamiam 6 · 0 1

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