1.

What is the least value of tan2 θ + cot2 θ + sin2 θ + cos2 θ + sec2 θ + cosec2 θ?1). 12). 53). 34). 7

Answer»

Using these trigonometric identities:

sin2 θ + cos2 θ = 1

tan2 θ + 1 = sec2 θ

cot2 θ + 1 = cosec2 θ

Required value: tan2 θ + cot2 θ + sin2 θ + cos2 θ + sec2 θ + cosec2 θ

On SIMPLIFYING we get:

⇒ tan2 θ + cot2 θ + 1 + 1 + tanθ + 1 + cot2 θ

⇒ 3 + 2(tan2 θ + cot2 θ)

Least value of tan2 θ + cot2 θ = 2

⇒ 3 + 2(2) =7



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