Question: What is the minimum value of sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ?Answer: sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ= (sin²θ + cosec²θ) + (cos²θ + sec²θ) + (tan²θ + cot²θ) Applying AM-GM logic, [i.e. (a + b) ≥ 2 √a*√b]: Minimum value = (2√ sin²θ *√cosec²θ) + (2√ cos²θ *√ sec²θ) + (2√ tan²θ *√ cot²θ) = (2√1) + (2√1) + (2√1) = 2 + 2 + 2 = 6Is it correct?
Question: What is the minimum value of sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ?
Answer:
sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ
= (sin²θ + cosec²θ) + (cos²θ + sec²θ) + (tan²θ + cot²θ)
Applying AM-GM logic, [i.e. (a + b) ≥ 2 √a*√b]:
Minimum value = (2√ sin²θ *√cosec²θ) + (2√ cos²θ *√ sec²θ) + (2√ tan²θ *√ cot²θ)
= (2√1) + (2√1) + (2√1)
= 2 + 2 + 2
= 6
Is it correct?
Avik Chattopadhyay , 8 Years ago
Grade 12th pass
