Evaluate the following: $\sin 45^\circ \sin 30^\circ + \cos 45^\circ \cos 30^\circ $
Last updated date: 24th Mar 2023
•
Total views: 310.5k
•
Views today: 5.87k
Answer
310.5k+ 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
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
