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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If \[1+2\,si{{n}^{2}}\theta \,\,co{{s}^{2}}\theta =si{{n}^{2}}\theta +co{{s}^{2}}\theta +4\,k\,\,si{{n}^{2}}\theta \] \[co{{s}^{2}}\theta \] what is the value of k?

    A)  1                                

    B)  ? 1           

    C)  \[\frac{1}{2}\] 

    D)  \[\frac{-1}{2}\]

    Correct Answer: C

    Solution :

    (c): \[1+2{{\sin }^{2}}\theta {{\cos }^{2}}\theta =1+4k{{\sin }^{2}}\theta {{\cos }^{2}}\theta \] \[\Rightarrow \]   \[0={{\sin }^{2}}\theta {{\cos }^{2}}\theta (4k-2)\] \[\Rightarrow \]   \[0=4K-2\] \[\Rightarrow \]   \[K=\frac{1}{2}\]                      


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