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  5. Introduction to Trigonometry

10th Class Mathematics Introduction to Trigonometry Question Bank Introduction to Trigonometry

  • question_answer
    If \[\sin x+{{\sin }^{2}}x=1,\] then \[{{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x=\_\_\_\_\_.\]

    A) 0                                 

    B) \[-1\]   

    C)  1                    

    D)         2        

    Correct Answer: C

    Solution :

    \[\sin x+{{\sin }^{2}}x=1\] \[\Rightarrow \]  \[\sin x=1-{{\sin }^{2}}x\,\,\,\Rightarrow \,\,\,\,\sin x={{\cos }^{2}}x\] Now, \[{{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x\] \[={{\sin }^{4}}x+2{{\sin }^{3}}x+{{\sin }^{2}}x\] \[={{({{\sin }^{2}}x+\sin x)}^{2}}=1\]\[[\because \,\,\,\,(\sin x+{{\sin }^{2}}x)=1]\]


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