Question

1/1-tan^2theta -1/1-cot^2theta=1
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Answer 1

/* There is a mistake in the question */

/*Sign between the two given fractions must be "+" */

$LHS = \frac{1}{1-tan^{2}\theta} +\frac{1}{1-cot^{2}\theta}\\= \frac{1}{1-tan^{2}\theta} + \frac{1}{1-\frac{1}{tan^{2}\theta}}\\= \frac{1}{1-tan^{2}\theta} + \frac{tan^{2}\theta}{tan^{2}\theta - 1}\\= \frac{1}{1-tan^{2}\theta} -\frac{tan^{2}\theta}{1-tan^{2}\theta}\\= \frac{1-tan^{2}\theta}{1-tan^{2} \theta} \\= 1 \\= RHS$

Therefore.,

$\red{\frac{1}{1-tan^{2}\theta} +\frac{1}{1-cot^{2}\theta}}\green {= 1}$

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