Evaluate the following: $\sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ $
Answer
384.9k+ views
Hint: Use direct values of angles of sin and cos
As we know the value of$\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$, the value of$\sin 30^\circ = \dfrac{1}{2}$, and the value of$\cos 30^\circ = \dfrac{{\sqrt 3 }}{2}$,
so, substitute these values in the given equation we have
$ \Rightarrow \sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ = \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{1}{2}} \right) + \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{{\sqrt 3 }}{2}} \right)$
$ = \dfrac{1}{{2\sqrt 2 }}\left( {1 + \sqrt 3 } \right)$
So, this is the required answer.
Note: - In such types of questions the key concept we have to remember is that we always remember all the standard angle values of sin and cosine, it will help us a lot in finding the required answer, so directly substitute these values we will get the required answer.
As we know the value of$\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$, the value of$\sin 30^\circ = \dfrac{1}{2}$, and the value of$\cos 30^\circ = \dfrac{{\sqrt 3 }}{2}$,
so, substitute these values in the given equation we have
$ \Rightarrow \sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ = \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{1}{2}} \right) + \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{{\sqrt 3 }}{2}} \right)$
$ = \dfrac{1}{{2\sqrt 2 }}\left( {1 + \sqrt 3 } \right)$
So, this is the required answer.
Note: - In such types of questions the key concept we have to remember is that we always remember all the standard angle values of sin and cosine, it will help us a lot in finding the required answer, so directly substitute these values we will get the required answer.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which planet is known as the red planet aMercury bMars class 6 social science CBSE

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE
