Question

If tan θ + cot θ = 2 , then tan square θ + cot square θ = ?

Answer 1

(tan∅+cot∅)²=2²
tan²∅+cot²∅+2tan²∅cot²∅=4
tan²∅+cot²∅=4-2
tan²∅+cot²∅=2

Answer 2

$tan θ + cot θ = 2$

$squaring \: both \: sides$

$(tan θ + cot θ) {}^{2} =( 2) {}^{2}$

$tan^{2} θ+cot^{2}θ +2 \times tan θ \times cot θ = 2$

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

$tan^{2} θ+cot^{2}θ +2 = 2$

$tan^{2} θ+cot^{2}θ = 2 - 2$

$\blue{tan^{2}θ+cot^{2}θ=0}$