Question
Prove that:
$\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos180^\circ=0$
$\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos180^\circ=0$
✓
Answer
$\text{L.H.S.}=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos180^\circ$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\cos90^\circ\times\dots\cos180^\circ$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\times0\times\dots\cos180^\circ$
$=0$
$=\text{R.H.S.}$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\cos90^\circ\times\dots\cos180^\circ$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\times0\times\dots\cos180^\circ$
$=0$
$=\text{R.H.S.}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.
Form the quadratic equation if its roots are
0 and -4
0 and -4
A lawn is in the from of a rectangle whose sides are in the ratio $5 : 3$ and its area is $3375\ m^2$. Find the cost of fencing the lawn at $₹ 20$ per meter.
→$\triangle ABC ~ \triangle PBQ$. In $\triangle ABC, AB = 3 cm, \angle B = 90^\circ, BC = 4 cm$. Ratio of the corresponding sides of two triangles is $7: 4$. Then construct $\triangle ABC$ and $\triangle PBQ$
→In the following figure find the area of the shaded region. $\big(\text{Use }\pi=3.14\big)$
→A well with 10m inside diameter is dug 8.4m deep. Earth taken out of it is spread all around it to a width of 7.5m to form an embankment. Find the height of the embankment.
Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm and 30 cm respectively. How many balls were melted to make the tube?
From the information, prepare the tax invoice for business to customer. (B2C)
Write any name, address, date, etc.
Supplier: M/s _____ Address ______ Date _____.
Invoice No. _______ GSTIN ______ .
Name of products:
(i) Jam bottle ₹ 75,1 piece, Rate of GST $12 \%$, HSN1207
(ii) Honey bottle ₹ 60, 1 piece, Rate of GST $5 \%$, HSN3607
(iii) Perfume bottle ₹ 225, 1 piece, Rate of GST $18 \%$, HSN9319
→Write any name, address, date, etc.
Supplier: M/s _____ Address ______ Date _____.
Invoice No. _______ GSTIN ______ .
Name of products:
(i) Jam bottle ₹ 75,1 piece, Rate of GST $12 \%$, HSN1207
(ii) Honey bottle ₹ 60, 1 piece, Rate of GST $5 \%$, HSN3607
(iii) Perfume bottle ₹ 225, 1 piece, Rate of GST $18 \%$, HSN9319
Find the value of k for which the following systems of linear equations has an infinite number of solutions:
$(k - 3)x + 3y = k,$
$kx + ky = 12$
→$(k - 3)x + 3y = k,$
$kx + ky = 12$
Find the values of following determinants.
(1) $\left|\begin{array}{cc}-1 & 7 \\ 2 & 4\end{array}\right|$
(2) $\left|\begin{array}{cc}5 & 3 \\ -7 & 0\end{array}\right|$
(3)$\left|\begin{array}{cc}\frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2}\end{array}\right|$
→(1) $\left|\begin{array}{cc}-1 & 7 \\ 2 & 4\end{array}\right|$
(2) $\left|\begin{array}{cc}5 & 3 \\ -7 & 0\end{array}\right|$
(3)$\left|\begin{array}{cc}\frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2}\end{array}\right|$