Question

cos 1º. cos 2°. cos 3°......... cos 100° =
a) sin 90°
b) cos 90°
c)0
d) 1​

Answer 1

Answer:

cos90° =0

and all terms are multiplied by cos90° too

So the value of expression = 0

which is the required ans

Answer 2

To Find

Value of cos 1° . cos 2° . cos 3° . ..... .cos 100°

Solution

We know that ,

$\bullet\ \; \sf cos\ 0^{\circ}=1$

$\bullet\ \; \sf \pink{cos\ 90^{\circ}=0}\ \; \bigstar$

$\to\ \sf cos\ 1^0.cos\ 2^0.cos\ 3^0.....\ cos\ 100^0$

$\to \sf cos\ 1^0.cos\ 2^0.cos\ 3^0...\ cos\ 90^0...\ cos\ 100^0$

$\to \sf cos\ 1^0.cos\ 2^0.cos\ 3^0...(0)...cos\ 100^0$

$\to\ \sf 0\ \; \bigstar$

So , Option C is correct

More Info

$\begin{gathered}\bullet\:\bf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}\end{gathered}$