Maths · Trigonometrical identities and trigonometrical functions
The value of is always
The value of \( \sin ^{2} \alpha+\operatorname{cosec}^{2} \alpha \) is always
- A. greater than 1
- B. less than 1
- C. greater than or equal to 2
- D. equal to 2
Step-by-step solution
For sin α ≠ 0, sin² α > 0. By AM-GM inequality, sin² α + csc² α ≥ 2√(sin² α · csc² α) = 2, with equality when sin² α = 1. Thus the expression is always ≥ 2.
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