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If this is solved you will be awarded a high mark prove the following formula 1 + sec²=cot²​

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This relationship is not true.


1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)

and


\cot^2(x) = \frac1{\tan^2(x)}

Rewrite the equation in terms of only tangent.


2 - \tan^2(x) = \frac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0

Factorize the left side.


\left(\tan^2(x) - 1\right)^2 = 0

Solve for
\tan(x).


\tan^2(x) - 1 = 0


\tan^2(x) = 1


\tan(x) = \pm 1


x = \pm\tan^(-1)(1) + n\pi = \pm\frac\pi4 + n\pi

where
n is an integer. That is, the equation only holds for certain values of
x, as opposed to all
x, so it's not an identity.

User TWGerard
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