Question
Write the value of $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ.$

Answer

Given that: $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos89^\circ\cos90^\circ\cos91^\circ\dots\cos179^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos89^\circ\times0\dots\cos179^\circ\cos180^\circ$
$=0$ $\big[\cos90^\circ=0\big]$
Hence the value of $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ\text{ is }0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Is 5, 8, 11, 14, …. an A.P.? If so then what will be the 100th term? Check whether 92 is in this A.P.? Is number 61 in this A.P.?
The inner and outer radii of a hollow cylinder are $15\ cm$ and $20\cm$, respectively. The cylinder is melted and recast into a solid cylinder of the same height.
Find the radius of the base of new cylinder.
Find the coordinates of the point on Y-axis which is equidistant from the points M(6, 5) and point N(-4, 3).
A box contains 3 apples, 4 oranges and 5 bananas. One fruit is drawn at random from the box. Write $S, n(S)$ and sample points of each of the following events.
Event A: Fruit is orange or banana
Event B: Fruit is not an apple.
Event C: Fruit is neither apple nor banana
Event D : Fruit is banana
'Sadhana Electronics' sold a dish washer to a customer. The total cost price including GST is ₹ 8960. The rate of GST on dish water is $28 \%$Find (i) Amount of GST (ii) Amount of SGST (iii) Taxable price
Find a relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(3, 6)$ and $(-3, 4).$
From the top of a building, an observer is looking at a scooter parked at some distance away, makes an angle of depression of $30^{\circ}$. If the height of the building is $40 \mathrm{~m}$, find how far the scooter is from the building. $(\sqrt{3}=1.73)$
Find the consecutive even integers whose squares have the sum $340$.
Find the sum of first 20 terms of the sequence whose $n^{\text {th }}$ term is $a_n=A n+B$.
A box contains 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box, find the probability that it bears:
  1. A two digit number.
  2. A perfect square number.
  3. A number divisible by 5.