Question

8. If tan thita+ cot thita - 2, then tan^2 thita + cot^2 thita​

Answer 1

Answer:

tanθ+cotθ=2

Squaring both sides;

(tanθ+cotθ)

2

=2

2

⇒tan

2

θ+cot

2

θ+2tanθcotθ=4

⇒tan

2

θ+cot

2

θ+2=4

⇒tan

2

θ+cot

2

θ=2

Answer 2

Answer:

Answer:-

$\sf\begin{gathered} \sf \: Value \: of \\ \sf \: tan^{2}\theta+cot^{2}\theta = 2\end{gathered}$

Step-by-step explanation:-

$\sf \: Given \: \sf \: tan\theta+cot\theta=2\:---(1)$

On Squaring both sides of the equation, we get

$\sf\left(tan\theta+cot\theta\right)^{2}=2^{2}$

$\sf \: \implies tan^{2}\theta+cot^{2}\theta+2 tan\theta \: cot\theta = 4$

$\sf\implies tan^{2}\theta+cot^{2}\theta+2 \times 1 = 4$

tanAcotA = 1

$\sf \implies tan^{2}\theta+cot^{2}\theta = 4-2$

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

Therefore,

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