10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    Find the minimum value of\[\text{cose}{{\text{c}}^{\text{2}}}\theta +\text{si}{{\text{n}}^{\text{2}}}\theta \].

    A)  0                            

    B)         - 1

    C)  1                            

    D)         2  

    Correct Answer: D

    Solution :

     \[\text{cose}{{\text{c}}^{2}}\theta +{{\sin }^{2}}\theta =\frac{1}{{{\sin }^{2}}\theta }+{{\sin }^{2}}\theta \] \[={{\left( \frac{1}{\sin \theta }-\sin \theta  \right)}^{2}}+2\] \[\therefore \] Minimum value of \[(\text{cose}{{\text{c}}^{2}}\theta +{{\sin }^{2}}\theta )=2\] [because the minimum value of \[{{\left( \frac{1}{\sin \theta }-\sin \theta  \right)}^{2}}\]0]


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