NCERT Solutions For Class 11 Maths chapter-3 Trigonometric Functions Exercise 3.4

Academic team of Physics Wallah developed step by step NCERT Solutions For Class-11 Maths Chapter 3 Trignometric Functions (Ex 3.4) Exercise 3.4 according to recommendations and Guideline of CBSE Read chapter 3 theory make sure you have gone through the theory part of chapter 3 from NCERT textbook and you have learned the formula of the given chapter. You can download solution of all chapters from Physics Wallah NCERT solutions of class 11.

NCERT Solutions for Class-11 Maths Exercise 3.4

Find the principal and general solutions of the following equations:

Question1. tan x = √3

Solution :
Given: tan x = √3Here lies in first or third quadrant.

tan x = √3
We know that  tan π/ 3 = √3
and tan(4 π/ 3)=tan( π + π / 3)=tan π / 3 = √3
Therefore, the principal solutions are x = π /3
 and 4π / 3
Now, tan x = tan π/ 3
Which implies,
x=nπ + π / 3
where n∈Z
Therefore, the general solution is x=n π + π /3
, where n∈Z .

Question2. Sec x = 2

Solution :

Question3. Cot x = −√3

Solution :

cot x = -√3
 Now we know that  cot π / 6 = √3

And cot( π - π /6) = -cot π/ 6

                 =-3–√
and  cot(2 π - π 6)=-cot π 6

                          =-√3
Therefore we have,

cot5π / 6 = -√3
and cot 11π/ 6=-√3

Therefore, the principal solutions are x=5 π/ 6
 and 11 π /6
Now, cot x = cot5 π/ 6
And we know cot x=1 / tan x

Therefore we have,

tan x = tan5 π / 6

Which implies,

x = n π + 5 π /6
 , where n∈Z

Therefore, the general solution is x=nπ + 5 π /6
 , where n∈Z .

Question4. Cosec x = -2

Solution :
Given: Cosec x = -2

cosec π/6 = 2

and

Therefore, the general solution is x=n π +(-1)ⁿ 7π / 6  ,where n∈Z.

Question5. Find the general solution for each of the following equations: cos 4 x = cos 2 x

Solution :
Given: cos 4 x = cos 2 x

Question6. Find the general solution for each of the following equations: cos 3x + cos x – cos 2x = 0

Solution :
Given: cos 3x + cos x – cos 2x = 0

Question7. Find the general solution for each of the following equations: sin 2x + cos x = 0

Solution :
Given: sin 2x + cos x = 0

Now we know that, sin 2x = 2sin x cos x
Therefore we have,
2sinx  cos x + cos x=0
Which implies,

     cos x(2sin x+1)=0

Therefore we have,

Either cos x=0
 or sin x = -1/2

Hence  we have ,

x = (2n + 1) π /2 , where n ∈ Z

Question8. Find the general solution for each of the following equations: sec² 2x = 1−tan 2x

Solution :
Given: sec² 2x = 1−tan 2x

Now we know that

sec² 2x - tan ²x = 1

Ther for we have ,

sec² 2x = 1− tan 2x

Question9. Find the general solution for each of the following equations: sin x + sin 3x + sin 5x = 0

Solution :
Given: sin x + sin 3x + sin 5x = 0