Question

if tan theta + 1/tan theta = 2 then what is the value of cosec theta.​

Answer 1

To find: $cosec\theta$

Step-by-step explanation:

Given, $tan\theta+\dfrac{1}{tan\theta}=2$

$\Rightarrow \dfrac{tan^{2}\theta+1}{tan\theta}=2$

$\Rightarrow tan^{2}\theta+1=2\:tan\theta$

$\Rightarrow tan^{2}\theta-2\:tan\theta+1=0$

$\Rightarrow (tan\theta-1)^{2}=0$

$\Rightarrow tan\theta-1=0$

$\Rightarrow tan\theta=1$

$\Rightarrow tan\theta=tan45^{\circ}$

$\Rightarrow \theta=45^{\circ}$

Now, $cosec\theta$

$=cosec45^{\circ}$

$=\sqrt{2}$

Answer: $cosec45^{\circ}=\sqrt{2}$

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Answer 2

Answer:

• tan theta + 1/tan theta =2
• tan 2 theta/1+tan theta =2
• theta =45
• cosec theta 45= root2
• √2 ans