जर  tanθ + cotθ = √3 चे मूल्य असल्यास, तर tan6θ + cot6θ चे मूल्य शोधा.

  1. -2
  2. -1
  3. -3
  4. -4

Answer (Detailed Solution Below)

Option 1 : -2
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
25 Qs. 50 Marks 12 Mins

Detailed Solution

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दिलेल्याप्रमाणे:

tanθ + cotθ = √3

वापरलेले सूत्र:

a3 + b3 = (a + b)3 - 3ab(a + b)

a2 + b2 = (a + b)2 - 2(a × b)

tanθ × cotθ = 1

गणना:

tanθ + cotθ = √3

दोन्ही बाजूंचा घन केल्यास, आपल्याला मिळते 

(tanθ + cotθ)3 = (√3)3

⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3

⇒ tan3θ + cot3θ + 3√3  = 3√3

⇒ tan3θ + cot3θ = 0  

दोन्ही बाजूंचा वर्ग घेतल्यास 

(tan3θ + cot3θ)2 = 0

⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0

⇒ tan6θ + cot6θ + 2 = 0    

⇒ tan6θ + cot6θ = - 2

∴ tan6θ + cot6θ चे मूल्य - 2 आहे.

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