Find the value of $x$in the following:
$\tan x = \sin 45^\circ \cos 45^\circ + \sin 30^\circ $
Answer
364.8k+ views
Hint: - Use $\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$
Given equation is
$\tan x = \sin 45^\circ \cos 45^\circ + \sin 30^\circ $
As we know
$\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$, and $\sin 30^\circ = \dfrac{1}{2}$
Substitute these values in the given equation
$
\Rightarrow \tan x = \sin 45^\circ \cos 45^\circ + \sin 30^\circ \\
\Rightarrow \tan x = \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{1}{{\sqrt 2 }}} \right) + \dfrac{1}{2} \\
$
As we have ${\text{ }}\left( {\sqrt 2 \times \sqrt 2 = 2} \right)$
$
\Rightarrow \tan x = \left( {\dfrac{1}{2}} \right) + \left( {\dfrac{1}{2}} \right) \\
\Rightarrow \tan x = \dfrac{{1 + 1}}{2} = \dfrac{2}{2} = 1 \\
$
Now we know $\tan 45^\circ = 1$
$
\Rightarrow \tan x = 1 = \tan 45^\circ \\
\Rightarrow x = 45^\circ \\
$
So, this is the required answer.
Note: -In such types of questions the key point we have to remember is that always remember all standard angle values of ${\text{sin, cosine and tan}}$, then simplify the given equation using these values we will get the required answer.
Given equation is
$\tan x = \sin 45^\circ \cos 45^\circ + \sin 30^\circ $
As we know
$\sin 45^\circ = \cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$, and $\sin 30^\circ = \dfrac{1}{2}$
Substitute these values in the given equation
$
\Rightarrow \tan x = \sin 45^\circ \cos 45^\circ + \sin 30^\circ \\
\Rightarrow \tan x = \left( {\dfrac{1}{{\sqrt 2 }}} \right)\left( {\dfrac{1}{{\sqrt 2 }}} \right) + \dfrac{1}{2} \\
$
As we have ${\text{ }}\left( {\sqrt 2 \times \sqrt 2 = 2} \right)$
$
\Rightarrow \tan x = \left( {\dfrac{1}{2}} \right) + \left( {\dfrac{1}{2}} \right) \\
\Rightarrow \tan x = \dfrac{{1 + 1}}{2} = \dfrac{2}{2} = 1 \\
$
Now we know $\tan 45^\circ = 1$
$
\Rightarrow \tan x = 1 = \tan 45^\circ \\
\Rightarrow x = 45^\circ \\
$
So, this is the required answer.
Note: -In such types of questions the key point we have to remember is that always remember all standard angle values of ${\text{sin, cosine and tan}}$, then simplify the given equation using these values we will get the required answer.
Last updated date: 26th Sep 2023
•
Total views: 364.8k
•
Views today: 7.64k
Recently Updated Pages
What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

What is the basic unit of classification class 11 biology CBSE

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

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
