11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[f(x)={{\cos }^{2}}x+{{\sec }^{2}}x,\] then  [MNR 1986]

    A) \[f(x)<1\]

    B) \[f(x)=1\]

    C) \[1<f(x)<2\]

    D) \[f(x)\ge 2\]

    Correct Answer: D

    Solution :

    Since \[{{\left( x-\frac{1}{x} \right)}^{2}}\ge 0,\,\,\text{}\,\,x\in R,\] we have \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\ge 2\] and Hence, \[f(x)={{\cos }^{2}}x+\frac{1}{{{\cos }^{2}}x}\ge 2\].


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