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Sin x + sin 3x+ sin …

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Sin x + sin 3x+ sin 5x = 0

    • Posted by Suman Chaudhary 4 years, 6 months ago

    CBSE > Class 11 > Mathematics
    • 2 answers

    Suman Chaudhary 4 years, 6 months ago

    Thanks

    1Thank You

    Jagdish 4 years, 6 months ago

    sinx + sin3x + sin5x = 0 »(sinx + sin5x) + sin3x = 0 Using the formula sinA + sinB = 2sin(A+B/2)cos(A-B/2) we get »2sin3x*cos2x + sin 3x = 0 Taking sin3x common, »sin3x(2cos2x+1) = 0 »sin3x = 0 or 2cos2x+1 = 0 sin 3x = sin 0 or cos2x = -1/2 » 3x = nπ + (-1)^n (0) or cos2x = cos 2π/3 » x = nπ/3 or x = (2nπ ± 2π/3)/2 » x = nπ/3 or x = nπ ± π/3

    2Thank You

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