Question

1. The value of cos 0°. cos 1°. cos 2°. cos 3°... Cos

89° cos 90° is​

Answer 1

Final answer: The value of $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$ is zero.

Given that: We are given multiplication series:$cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$

To find: We have to find the value of $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$.

Explanation:

• Here we have find the final answer of the given multiplication series:

$cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$

• In this given multiplication series, last term is $cos (90\°)$.

• We all know the value of $cos (90\°)$ is zero.

$cos (90\°) = cos(\frac{\pi }{4}) = 0$

• Substitute the value of  $cos (90\°)$ in the multiplication series.

Then,

$cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°) = cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* 0$

• In general if any number is multiplied to zero, the answer will be zero.
• Therefore $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$ is multiplied to zero the answer will be zero.

i.e. $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* 0 = 0$

• $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)=0$

Hence, the value of $cos (0\°) * cos (1\°)* cos (2\°)* cos (3\°)... cos(89\°)* cos (90\°)$ is zero.

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Answer 2

The value of cos 0°. cos 1°. cos 2°. cos 3°... cos 89° cos 90° = 0

Given :

The expression cos 0°. cos 1°. cos 2°. cos 3°... cos 89° cos 90°

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

cos 0°. cos 1°. cos 2°. cos 3°... cos 89° cos 90°

Step 2 of 2 :

Find the value of the expression

cos 0°. cos 1°. cos 2°. cos 3°... cos 89° cos 90°

= cos 0°× cos 1° × cos 2° × cos 3° × ... × cos 89° × cos 90°

= cos 0°× cos 1° × cos 2° × cos 3° × ... × cos 89° × 0 [ ∵ cos 90° = 0 ]

= 0

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