Question

F(x)=(sinx + cosecx)^2+(cosx + secx)^2, what is the minimum value of f(x)

Answer 1

F(x) = sin²x + cosec²x + 2 + cos²x + sec²x + 2
= (sin²x + cos²x) + 4 + cosec²x + sec²x
= 1 + 4 + (1 + tan²x) + (1 + cot²x)
= 7 + tan²x + cot²x
= 7 + 1 + 1 {min value is when x is π/4}
= 9

Answer 2

Answer:

F(x) = sin²x + cosec²x + 2 + cos²x + sec²x + 2

= (sin²x + cos²x) + 4 + cosec²x + sec²x

= 1 + 4 + (1 + tan²x) + (1 + cot²x)

= 7 + tan²x + cot²x

= 7 + 1 + 1 {min value is when x is π/4}

= 9

Step-by-step explanation:

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