If sinθ + cosθ =(√(11))/3 , then what is tanθ + cotθ equal to :

If sinθ + cosθ =(√(11))/3 , then what is tanθ + cotθ equal…

If $sinθ + cosθ =\frac{ \sqrt{11}}{3}$ , then what is tanθ + cotθ equal to :

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Correct answer: B

Explanation

The correct answer i option 2 i.e. 9.

sinθ + cosθ = √11/3

⇒ (sinθ + cosθ)² = 11/9

⇒ 1 + 2 sinθ cosθ = 11/9

⇒ 2 sinθ cosθ = 2/9

⇒ sinθ cosθ = 1/9

Now, tanθ + cotθ = (sinθ/cosθ) + (cosθ/sinθ)

= (sin²θ + cos²θ)/(sinθ cosθ)

= 1/(1/9)

= 9