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?

Avik Chattopadhyay , 6 Years ago

Grade 12th pass