Answer
Verified
478.2k+ views
Hint: Here we have to use the values of trigonometric ratios for a particular angle. And we have to use one property that is multiplication of anything with 0 is always 0.
Complete step-by-step answer:
As you can see in \[\cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }.......\cos {180^ \circ }\]
It is product of cosine of all angle from ${1^ \circ }$ to ${180^ \circ }$
In which ${30^ \circ },{45^ \circ },{60^ \circ },{90^ \circ }$ etc, most angles come as you know the value of the cosine of these angles.
AS you know the value of
$\cos {30^ \circ } = \dfrac{{\sqrt 3 }}{2},\cos {45^ \circ } = \dfrac{1}{{\sqrt 2 }},\cos {60^ \circ } = \dfrac{1}{2},\cos {90^ \circ } = 0$
We can write question like this
\[ \Rightarrow \cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }......\cos {30^ \circ }....\cos {45^ \circ }....\cos {60^ \circ }.....\cos {90^ \circ }.....\cos {180^ \circ }\]
All values are in multiply so you know value of $\cos {90^ \circ } = 0$
\[ \Rightarrow \cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }......\cos {30^ \circ }....\cos {45^ \circ }....\cos {60^ \circ }..... \times 0 \times .....\cos {180^ \circ }\]
As you know the multiple of 0 from any number then result comes to 0
$ \Rightarrow 0$
Answer is 0.
So, the correct option is (b).
Note: Whenever you come to these type of problem you have to use known value of trigonometric angle (like \[\sin {30^ \circ },\tan {45^ \circ }\] etc) and try to use these values in equation after some rearrangement then you can easily get answer.
Complete step-by-step answer:
As you can see in \[\cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }.......\cos {180^ \circ }\]
It is product of cosine of all angle from ${1^ \circ }$ to ${180^ \circ }$
In which ${30^ \circ },{45^ \circ },{60^ \circ },{90^ \circ }$ etc, most angles come as you know the value of the cosine of these angles.
AS you know the value of
$\cos {30^ \circ } = \dfrac{{\sqrt 3 }}{2},\cos {45^ \circ } = \dfrac{1}{{\sqrt 2 }},\cos {60^ \circ } = \dfrac{1}{2},\cos {90^ \circ } = 0$
We can write question like this
\[ \Rightarrow \cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }......\cos {30^ \circ }....\cos {45^ \circ }....\cos {60^ \circ }.....\cos {90^ \circ }.....\cos {180^ \circ }\]
All values are in multiply so you know value of $\cos {90^ \circ } = 0$
\[ \Rightarrow \cos {1^ \circ } \cdot \cos {2^ \circ } \cdot \cos {3^ \circ }......\cos {30^ \circ }....\cos {45^ \circ }....\cos {60^ \circ }..... \times 0 \times .....\cos {180^ \circ }\]
As you know the multiple of 0 from any number then result comes to 0
$ \Rightarrow 0$
Answer is 0.
So, the correct option is (b).
Note: Whenever you come to these type of problem you have to use known value of trigonometric angle (like \[\sin {30^ \circ },\tan {45^ \circ }\] etc) and try to use these values in equation after some rearrangement then you can easily get answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE