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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If A, B, C and D are the angles of a quadrilateral , then sin (A + B) + sin (C + D) is equal to

    A) 1                    

    B) - 1

    C) 0

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

    Correct Answer: C

    Solution :

     Since A, B, C, D are the angles of a quadrilateral, \[{{A}^{o}}+{{B}^{o}}+{{C}^{o}}+{{D}^{o}}=2\pi \]                 \[\therefore \]  \[\sin (A+B)+\sin (C+D)\]                 \[=2\sin \,\frac{A+B+C+D}{2}\,\cos \frac{A+B-C-D}{2}\]                 \[=2\,\sin \pi \cos \frac{A+B-C-D}{2}\]                 \[=2\times 0\times \cos \frac{A+B-C-D}{2}=0\]


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