Answer
Verified
425.1k+ views
Hint - In order to solve this problem use the formula that $\sin 2\theta = 2\sin \theta \cos \theta $. Then put the value of angle.
As we know the formula,
$\sin 2\theta = 2\sin \theta \cos \theta $ ……(i)
And the given equation is $2\cos 22{\dfrac{1}{2}^0}\sin 22{\dfrac{1}{2}^0}\,\,$
We also know $a\dfrac{b}{c} = \dfrac{{ac + b}}{c}$ ……(ii)
From (ii) we can say, $22\dfrac{1}{2} = \dfrac{{22(2) + 1}}{2} = \dfrac{{44 + 1}}{2} = \dfrac{{45}}{2}$ ……(iii)
Therefore the given equation can be written as ,
$2\cos {\dfrac{{45}}{2}^0}\sin {\dfrac{{45}}{2}^0}\,\,$
And from (i) we can say,
$2\cos {\dfrac{{45}}{2}^0}\sin {\dfrac{{45}}{2}^0}\,\, = \sin \dfrac{{2\,{\text{x }}45}}{2} = \sin {45^0}$
We know the value of sin45 is $\dfrac{1}{{\sqrt 2 }}$.
Therefore from the above equations we can say
$2\cos 22{\dfrac{1}{2}^0}\sin 22{\dfrac{1}{2}^0} = \dfrac{1}{{\sqrt 2 }}$.
Hence the answer to this question is $\dfrac{1}{{\sqrt 2 }}$.
Note – In these types of problems of trigonometry we have to use the general formula of trigonometry, after observing which formula can be fit into the given question then solve the equation according to the formula. There is an alternative method to solve this question , it is , if we know the values of the angle given in the equation we can also directly put it and get the actual value of the equation.
As we know the formula,
$\sin 2\theta = 2\sin \theta \cos \theta $ ……(i)
And the given equation is $2\cos 22{\dfrac{1}{2}^0}\sin 22{\dfrac{1}{2}^0}\,\,$
We also know $a\dfrac{b}{c} = \dfrac{{ac + b}}{c}$ ……(ii)
From (ii) we can say, $22\dfrac{1}{2} = \dfrac{{22(2) + 1}}{2} = \dfrac{{44 + 1}}{2} = \dfrac{{45}}{2}$ ……(iii)
Therefore the given equation can be written as ,
$2\cos {\dfrac{{45}}{2}^0}\sin {\dfrac{{45}}{2}^0}\,\,$
And from (i) we can say,
$2\cos {\dfrac{{45}}{2}^0}\sin {\dfrac{{45}}{2}^0}\,\, = \sin \dfrac{{2\,{\text{x }}45}}{2} = \sin {45^0}$
We know the value of sin45 is $\dfrac{1}{{\sqrt 2 }}$.
Therefore from the above equations we can say
$2\cos 22{\dfrac{1}{2}^0}\sin 22{\dfrac{1}{2}^0} = \dfrac{1}{{\sqrt 2 }}$.
Hence the answer to this question is $\dfrac{1}{{\sqrt 2 }}$.
Note – In these types of problems of trigonometry we have to use the general formula of trigonometry, after observing which formula can be fit into the given question then solve the equation according to the formula. There is an alternative method to solve this question , it is , if we know the values of the angle given in the equation we can also directly put it and get the actual value of the equation.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE