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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    \[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}{{\mathbf{6}}^{{}^\circ }}+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}{{\mathbf{6}}^{{}^\circ }}+.......+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{8}{{\mathbf{4}}^{{}^\circ }}+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{8}{{\mathbf{5}}^{{}^\circ }}=\]?

    A) \[39\frac{1}{2}\]

    B) \[40\frac{1}{2}\]

    C) 40

    D) \[49\frac{1}{\sqrt{2}}\]

    Correct Answer: B

    Solution :

    (b): \[(si{{n}^{2}}{{5}^{{}^\circ }}+co{{s}^{2}}{{5}^{{}^\circ }})+(si{{n}^{2}}{{6}^{{}^\circ }}\text{ }co{{s}^{2}}{{6}^{{}^\circ }})+........+\] \[\text{to}\,40\,\text{terms}+\text{si}{{\text{n}}^{\text{2}}}{{45}^{{}^\circ }}=40+{{\left( \frac{1}{\sqrt{2}} \right)}^{2}}=40+\frac{1}{2}\]\[=40\frac{1}{2}\]


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