Question
Download Solution PDFFind the value of cos 1°cos 2°cos 3°cos 4°..... cos 900°?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Given:
The product: cos 1° × cos 2° × cos 3° × ... × cos 900°
Concept Used:
The cosine function (cos θ) is periodic with a period of 360°.
This means: cos(θ) = cos(θ + 360k), where k is any integer.
Additionally, the cosine function has a zero value at specific angles.
For example: cos(90°) = 0
If any term in the product becomes 0, the entire product evaluates to 0.
Calculation:
Observe the product: cos 1° × cos 2° × cos 3° × ... × cos 900°.
Among these terms, one of the angles is 90°. Specifically: cos(90°) = 0.
⇒ The entire product becomes: cos 1° × cos 2° × ... × cos 90° × ... × cos 900° = 0.
Conclusion:
∴ The value of the product is 0.
Last updated on Jul 1, 2025
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