Question

cos1°.cos2°.cos3°...............cos100°=​

Answer 1

We know,

$\boxed{cos 90^{\circ} = 0}$

☆When we multiply any number with zero(0), the answer is always zero (0).

For example,

• 40 × 0 = 0
• (20 + 16 + 1937) × 0 = 0

In the series, cos1°.cos2°.cos3°...............cos100°, cos90° is also included i.e.

=cos1°.cos2°.cos3°...............cos90° cos100°

=cos1°.cos2°.cos3°...............× 0 × cos100°

= 0

So the answer of the given series cos1°.cos2°.cos3°...............cos100°= 0

Answer 2

Given question.

$\cos1\textdegree\cdot\cos2\textdegree\cdot\cos3\textdegree\cdot\cos4\textdegree\cdot......\cdot\cos97\textdegree\cdot\cos98\textdegree\cdot\cos99\textdegree\cdot\cos100\textdegree$

First, we have to keep in mind that,

"cos 90° is multiplied within this!!!"

What is the value of  cos 90°?  It's none other than 0, isn't it?

So, since 0 is multiplied within it, won't the entire product be 0?!

We know, every number multiplied by 0 always results 0.

Hence the answer is also 0.

That's all!

$\boxed{\cos1\textdegree\cdot\cos2\textdegree\cdot\cos3\textdegree\cdot\cos4\textdegree\cdot......\cdot\cos97\textdegree\cdot\cos98\textdegree\cdot\cos99\textdegree\cdot\cos100\textdegree=\Large \bold{0}}$