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in Trigonometry by (32.2k points)
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If (tanθ + cotθ) = 5 then(tan2θ + cot2θ) = ? 

(a) 27 

(b) 25 

(c) 24 

(d) 23

1 Answer

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Best answer

Correct answer is (d) 23

We have (tan θ + cot θ) = 5 

Squaring both sides, we get: 

(Tan θ + cot θ)2 = 52 

⇒ tan2 θ + cot2 θ + 2 tan θ cot θ = 25 

⇒ tan2 θ + cot2 θ + 2 = 25   [∵ tan θ = 1/cotθ ] 

⇒ tan2 θ + cot2 θ = 25 − 2 = 23

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