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    Find the value ofcos1° cos2° cos3° ... cos89° cos90°.
    Question

    Find the value of

    cos1° cos2° cos3° ... cos89° cos90°.

    A.

    1

    B.

    12\frac{1}{\sqrt2}​​

    C.

    0

    D.

    12\frac{1}{2}​​

    Correct option is C

    Given:

    We are to evaluate the product:

    cos1cos2cos3cos89cos90\cos1^\circ \cdot \cos2^\circ \cdot \cos3^\circ \cdots \cos89^\circ \cdot \cos90^\circ​​

    Concept Used:
    cos90=0\cos90^\circ = 0​​

    Solution:
    Since cos90=0\cos90^\circ = 0​, the entire product becomes:

    cos1cos2cos890=0\cos1^\circ \cdot \cos2^\circ \cdot \cdots \cdot \cos89^\circ \cdot 0 = 0

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