Find the value of cos 1°cos 2°cos 3°cos 4°..... cos 900°?

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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.

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-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).

->The Exam will be held on 9th July 2025.

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

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