📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    If (sinx + siny) = a and (cosx + cosy) = b, then find

    the value of (sinx siny + cosx cosy). [A] (a²+b²-2)/ 2 [B] (a2-b2-2)/ 2 [C] (a²+b²-1)/ 2 [D](a²+b²+2)/2
    A B Correct Answer Incorrect Answer
    B C Correct Answer Incorrect Answer
    C D Correct Answer Incorrect Answer
    D A Correct Answer Incorrect Answer

    Solution

    (sinx + siny) = a          (both sides squaring). a2 =sin2x +sin2y +2sinx.siny   … (1) (cosx + cosy) = b        (both sides squaring). b2 =cos2x +cos2y+2cosx.cosy             … (2) Now EQ (1) +EQ (2) … (sin2x +sin2y +2sinx.siny) + cos2x +cos2y+2cosx.cosy =a2+b2 =1+1+2(sinx. siny+cosx. cosy) = a2+b2 2(sinx. siny+cosx. Cosy) = a2+b2-2 sinx. siny+cosx. Cosy = (a2+b2-2)/2.

    Practice Next
    More Trigonometry Questions

    Relevant for Exams:

    ask-question