8th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer The value of \[\mathbf{tan}{{\mathbf{4}}^{o}}.\mathbf{tan4}{{\mathbf{3}}^{o}}.\mathbf{tan4}{{\mathbf{7}}^{o}}.\mathbf{tan8}{{\mathbf{6}}^{o}}\]is

    A)  2                                

    B)  3              

    C)  1 

    D)  4

    Correct Answer: C

    Solution :

    (c): \[tan{{4}^{{}^\circ }}.tan{{43}^{{}^\circ }}.tan{{47}^{{}^\circ }}.tan{{86}^{{}^\circ }}\] \[=tan{{4}^{{}^\circ }}.tan{{43}^{{}^\circ }}.tan({{90}^{{}^\circ }}-{{43}^{{}^\circ }}).tan({{99}^{{}^\circ }}-{{4}^{{}^\circ }})\] \[=tan{{4}^{{}^\circ }}\times tan{{43}^{{}^\circ }}\times cot{{43}^{{}^\circ }}\times cot{{4}^{{}^\circ }}=1\] \[\left[ tan\left( {{99}^{{}^\circ }}-\theta  \right)=cot\theta ;tan\theta .cot\theta =1 \right]\]

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