Question

if tan theta+cot theta =1 then tan square theta +cot square theta is equal to?Please answer it fast. No spam ​

Answer 1

Step-by-step explanation:

as we know cota is equal to 1/tana

Answer 2

Answer:

$tan^{2}$ θ +  $cot^{2}$ θ = $-1$

Step-by-step explanation:

Given that, tanθ + cotθ = 1

We are expected to find,

                   $tan^{2}$ θ + $cot^{2}$ θ

Let us square tanθ + cotθ = 1  on both sides.

                      $(tan\theta+cot\theta)^{2} = 1^{2}$

Use the formula,  

                    $(a+b)^{2} = a^{2}+b^{2}+2ab$

Clearly, a=tanθ and b=cotθ

                          $(tan\theta+cot\theta)^{2}=1$

 $tan^{2}\theta+cot^{2}\theta+2*tan\theta*cot\theta=1$

We know that the reciprocal of    $cot\theta=\frac{1}{tan\theta}$

∴ $tan^{2}\theta+cot^{2}\theta+2*tan\theta*\frac{1}{tan\theta} =1$

                       $tan^{2}\theta+cot^{2}\theta+2=1$

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

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

  ∴  $tan^{2}\theta+cot^{2}\theta=-1$ is the required solution.

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