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Q: If tan3θ.tan7θ = 1, where 7θ is an acute angle, then find the value of cot15θ
  • A.
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  • B. 1
  • C. -1
  • D.
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Correct Answer: Option C - tan3θ.tan7θ = 1 (where7θ is an acute angle) tan7θ = cot3θ tan7θ = tan(90° – 3θ) 7θ= 90° – 3θ then (3θ+7θ) = 90° 10θ = 90° θ = 9° then cot 15θ cot (15 x 9)° = cot 135° = cot (90x1+45°) = – tan 45° = –1
C. tan3θ.tan7θ = 1 (where7θ is an acute angle) tan7θ = cot3θ tan7θ = tan(90° – 3θ) 7θ= 90° – 3θ then (3θ+7θ) = 90° 10θ = 90° θ = 9° then cot 15θ cot (15 x 9)° = cot 135° = cot (90x1+45°) = – tan 45° = –1

Explanations:

tan3θ.tan7θ = 1 (where7θ is an acute angle) tan7θ = cot3θ tan7θ = tan(90° – 3θ) 7θ= 90° – 3θ then (3θ+7θ) = 90° 10θ = 90° θ = 9° then cot 15θ cot (15 x 9)° = cot 135° = cot (90x1+45°) = – tan 45° = –1