Question

If tan θ + cot θ = 5, find the value of tan 2θ + cot θ.
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Answer 1

Given data:

$tan\theta+cot\theta=5$

To find:

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

Step-by-step explanation:

Given, $tan\theta+cot\theta=5$

Squaring both sides, we get

$\quad (tan\theta+cot\theta)^{2}=5^{2}$

$\Rightarrow tan^{2}\theta+cot^{2}\theta+2\:tan\theta\:cot\theta=25$

• Used: $(a+b)^{2}=a^{2}+b^{2}+2ab$

$\Rightarrow tan^{2}\theta+cot^{2}\theta+2=25$

• Used: $tan\theta\:cot\theta=1$

$\Rightarrow tan^{2}\theta+cot^{2}\theta=23$

Answer:

$\quad tan^{2}\theta+cot^{2}\theta=23$

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Answer 2

Answer: 23

Step-by-step explanation:

Given,

tanθ+cotθ=5

Now squaring both sides we get,

⇒(tan

2

θ+cot

2

θ+2.tanθ.cotθ)=25

⇒tan

2

θ+cot

2

θ=25−2 [ Since tanθ.cotθ=1]

⇒tan

2

θ+cot

2

θ=23.

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