Question

Simple question for 25 points solve it right now
Solve tan²θ + cot²θ = 2

Answer 1

Hey friend here is ur answer-:

Answer 2

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• Solve the given equation.

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Given equation:-

$\boxed{ \sf \tan^{2} \theta + \cot^{2} \theta = 2 }$

$\sf\implies { \tan }^{2} \theta + \frac{1}{ { \tan }^{2} \theta } = 2$

$\sf let \: a = \tan \theta$

Therefore,

$\sf {a}^{2} + \frac{1}{ {a}^{2} } = 2$

$\sf \implies {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 0$

$\sf \implies {(a - \frac{1}{a} )}^{2} = 0$

$\sf \implies {(a - \frac{1}{a} )} = 0$

$\sf \implies a = \frac{1}{a}$

$\sf \implies {a}^{2} = 1$

$\sf \implies { \tan }^{2} \theta = 1$

$\sf \implies { \tan } \: \theta = 1$

$\sf \implies \theta = \tan^{ - 1} (1)$

$\sf \implies \theta = 45 \degree$

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• $\sf \theta = 45 \degree$