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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If \[\alpha +\beta =\text{9}0{}^\circ \] and \[\alpha =2\beta \], then \[\text{co}{{\text{s}}^{\text{2}}}\alpha +\text{si}{{\text{n}}^{\text{2}}}\beta \] equals to

    A) \[\frac{1}{2}\]                   

    B) 0

    C) 1

    D) 2

    Correct Answer: A

    Solution :

     \[\alpha =2\beta \] and \[\alpha +\beta ={{90}^{o}}\] \[\therefore \] \[\alpha ={{60}^{o}}\] and \[\beta ={{30}^{o}}\] \[\therefore \]  \[{{\cos }^{2}}\alpha +{{\sin }^{2}}\beta ={{\cos }^{2}}{{60}^{o}}+{{\sin }^{2}}{{30}^{o}}\]                 \[=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\]


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