Thank you for your prompt answer. But my doubt is not clear. According to the AM-GM inequality:1)a sin²θ + b cosec²θ≥ 2 √a*√b2)a cos²θ + b sec²θ≥ 2 √a*√b3)a tan²θ + b cot²θ≥ 2 √a*√bApplying these inequalities I get answer 6 which is lower than your answer 7. You have applied Pythagorean trigonometric identities first and then AM-GM inequality. So I think 6 is the minimum value. Please explain my mistakes.

Avik Chattopadhyay , 7 Years ago

Grade 12th pass