Answer
451.5k+ views
Hint: In this question, we use trigonometric values to solve problems. Like ${\text{cosec}}\left( {{{60}^0}} \right) = \dfrac{2}{{\sqrt 3 }},\cot \left( {{{30}^0}} \right) = \sqrt 3 $ and $\sec \left( {{{45}^0}} \right) = \sqrt 2$ put these trigonometric values in question and after some calculation we can get the required answer.
Complete step-by-step answer:
Given, ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$
As we know the some standard values of trigonometric angles,
${\text{cosec}}\left( {{{60}^0}} \right) = \dfrac{2}{{\sqrt 3 }},\cot \left( {{{30}^0}} \right) = \sqrt 3 $ and $\sec \left( {{{45}^0}} \right) = \sqrt 2 $
Put these trigonometric values in ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$
\[ \Rightarrow 3 \times {\left( {\dfrac{2}{{\sqrt 3 }}} \right)^2} - 2 \times {\left( {\sqrt 3 } \right)^2} + {\left( {\sqrt 2 } \right)^2}\]
Square the following values,
\[
\Rightarrow 3 \times \dfrac{4}{3} - 2 \times 3 + 2 \\
\Rightarrow 4 - 6 + 2 \\
\Rightarrow 6 - 6 \\
\Rightarrow 0 \\
\]
So, the value of ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$ is 0.
Note: Whenever we face such types of problems we use some important points. First we write the all values of trigonometric angles should be used in question, then put all trigonometric values in question. So, after some calculation we will get the required answer.
Complete step-by-step answer:
Given, ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$
As we know the some standard values of trigonometric angles,
${\text{cosec}}\left( {{{60}^0}} \right) = \dfrac{2}{{\sqrt 3 }},\cot \left( {{{30}^0}} \right) = \sqrt 3 $ and $\sec \left( {{{45}^0}} \right) = \sqrt 2 $
Put these trigonometric values in ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$
\[ \Rightarrow 3 \times {\left( {\dfrac{2}{{\sqrt 3 }}} \right)^2} - 2 \times {\left( {\sqrt 3 } \right)^2} + {\left( {\sqrt 2 } \right)^2}\]
Square the following values,
\[
\Rightarrow 3 \times \dfrac{4}{3} - 2 \times 3 + 2 \\
\Rightarrow 4 - 6 + 2 \\
\Rightarrow 6 - 6 \\
\Rightarrow 0 \\
\]
So, the value of ${\text{3cose}}{{\text{c}}^2}\left( {{{60}^0}} \right) - 2{\cot ^2}\left( {{{30}^0}} \right) + {\sec ^2}\left( {{{45}^0}} \right)$ is 0.
Note: Whenever we face such types of problems we use some important points. First we write the all values of trigonometric angles should be used in question, then put all trigonometric values in question. So, after some calculation we will get the required answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)