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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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