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If + =2, then the value of ^2 +^2 is __________?

Question

If $tan θ + cot θ = 2$ , then the value of $tan^{2} θ + cot^{2} θ$ is __________?

4

2

\frac{3}{2}

5

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tan θ + cot θ = 2

, then the value of

tan^{2} θ + cot^{2} θ

is __________?

8 mins ago

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8 mins ago

Text solutionVerified

Given,

tan θ + cot θ = 2

Squaring both sides, we get

(tan θ + cot θ)^{2} = 2^{2}

\Rightarrow tan^{2} θ + cot^{2} θ + 2 = 4

.....Since

tan θ \times cot θ = tan θ \times \frac{1}{tan θ} = 1

\Rightarrow tan^{2} θ + cot^{2} θ = 2

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Question Text	If $tan θ + cot θ = 2$ , then the value of $tan^{2} θ + cot^{2} θ$ is __________?
Answer Type	Text solution:1
Upvotes	150