Question

If tan θ + 1/ tan θ = 2, then the value of tan² θ + 1/ tan² θ is​

Answer 1

$\tan θ + \frac{1}{ \tanθ } = 2$

$\: {squaring \: both \: sides}$

$( \tan θ + \frac{1}{ \tanθ }) {}^{2} = (2) {}^{2}$

$\tan^{2} θ+\frac{1}{ \tan^{2}θ}+2 \times\tanθ \times\frac{1}{ \tanθ} = 4$

$( \tan θ + \frac{1}{ \tanθ }) {}^{2} + 2 = 4$

${ \tan}^{2}θ + \frac{1}{ { \tan }^{2}θ } = 4 - 2$

${ \tan}^{2}θ + \frac{1}{ { \tan }^{2}θ } = 2$

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