If 2cos 3theta =under root 3 ,then find the value of theta ?

Question

Answer

Its simple..

2 cos 3© = √3
cos 3© = (√3)/2.......(i)

nd we know that cos 30° = (√3) /2

or, cos 3 (10°) = (√3)/2.......(ii)

from (i) nd (ii) we got...
© = 10° answer !!

Answer

2Cos 3 tetha=√3,---> given

to find--> tetha=?

3cos tetha=√3/2,

3cos tetha=√3/2= cos30,( cos 30=√3/2),

3tetha=30,

tetha=30/3=10

Answer

Given: 2cos 3θ = √3

To find: Value of θ

Solution:

We know that,

cos 60° = 1/2 and cos 30° = √3/2

Using the formula of cos 3θ = 4cos³θ - 3cosθ, we can write:

cos 60° = cos (3 × 20°)

1/2 = 4 cos³ 20° - 3 cos 20°

Now, let's assume 3θ = 60°, which means θ = 20°.

Substituting θ = 20° in the above equation, we get:

cos 60° = cos 3θ

1/2 = 4 cos³ 20° - 3 cos 20°

1/2 = 4 (2cos 20°)³ - 3 (2cos 20°)

1/2 = 32 cos³ 20° - 24 cos 20°

Multiplying the above equation by 2, we get:

1 = 64 cos³ 20° - 48 cos 20°

Dividing the above equation by 16, we get:

1/16 = 4 cos³ 20° - 3 cos 20°

Now, let's assume 2cos 3θ = √3, which means:

2cos 3θ = √3

cos 3θ = √3/2

Substituting cos 3θ = √3/2 in the above equation, we get:

1/16 = 4 cos³ θ - 3 cos θ

Multiplying the above equation by 16, we get:

1 = 64 cos³ θ - 48 cos θ

Dividing the above equation by 16, we get:

1/16 = 4 cos³ θ - 3 cos θ

Comparing the above equation with the previous equation, we get:

4 cos³ θ - 3 cos θ = 4 cos³ 20° - 3 cos 20°

4 cos³ θ = 4 cos³ 20°

cos³ θ = cos³ 20°

Taking cube root on both sides, we get:

cos θ = cos 20°

Now, we know that cos θ = cos (360° - θ)

So, we have two possible values of θ:

θ = 20°

360° - θ = 340°

Hence, the two possible values of θ are 20° and 340°.

Answer

10

Answer

Let. .. theta sign...= ¶
2 cos 3 ¶ =√3
cos 3¶ =√3/2.

> but
we know that cos 30° =√3/2.

cos 3 ¶ = cos 30. •••• [ •.• both equal to √3/2 ]
¶ = cos 30°/ cos 3
¶= 10°

Similar Class 10 Doubts

If 7 sin Sq.theta 3 cos Sq theta =4 then show that tan theta =1/under root 3?

If sin Theta=c / Root under CSquare D square,where did greater than 0 the find the value of cos theta and tan theta.?

If root 3 tan 2 theta -3 = 0 then what is the value of theta?

Sin theata +sin²theata =1, then find the value of cos¹²theata + 3 cos10 theata+ 3 cos8 theata +cos6 theata+ 2cos⁴ theata +2 cos² theata-2?

Sin theata sin²theata =1, then find the value of cos¹²theata 3 cos10 theata 3 cos8 theata cos6 theata 2cos⁴ theata 2 cos2² theata-2?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company