NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions Ex 3.4
Page No 78:
Question 1:
Find the principal and general solutions of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m7dfb5870.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m7dfb5870.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m7dfb5870.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_54775535.gif)
Therefore, the principal solutions are x =
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m3d560eca.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m478dcfb5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_m5798c255.gif)
Therefore, the general solution is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_463bfd8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5523/Chapter%203_html_463bfd8.gif)
Question 2:
Find the principal and general solutions of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_5585b76e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_5585b76e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_5585b76e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_m60f4c5af.gif)
Therefore, the principal solutions are x =
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_m3d560eca.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_404dfc18.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_m713ed688.gif)
Therefore, the general solution is
, where n ∈ Z
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5524/Chapter%203_html_m1b31190.gif)
Question 3:
Find the principal and general solutions of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_m29b289a5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_m29b289a5.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_m29b289a5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_54313646.gif)
Therefore, the principal solutions are x =
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_m371b1b16.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_4bcb2f59.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_3ee1bf23.gif)
Therefore, the general solution is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_2b1760fb.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5525/Chapter%203_html_2b1760fb.gif)
Question 4:
Find the general solution of cosec x = –2
Answer:
cosec x = –2
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5657/Ch-3_html_6f7c9dae.gif)
Therefore, the principal solutions are x =
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5657/Ch-3_html_70a26da4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5657/Ch-3_html_m756f03a.gif)
Therefore, the general solution is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5657/Ch-3_html_c39d8f9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5657/Ch-3_html_c39d8f9.gif)
Question 5:
Find the general solution of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5527/Chapter%203_html_34f7e2cf.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5527/Chapter%203_html_34f7e2cf.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5527/Chapter%203_html_34f7e2cf.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5527/Chapter%203_html_31d7b9a8.gif)
Question 6:
Find the general solution of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5528/Chapter%203_html_21edf56f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5528/Chapter%203_html_21edf56f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5528/Chapter%203_html_21edf56f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5528/Chapter%203_html_m7ccb335.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5528/Chapter%203_html_m62ddbb96.gif)
Question 7:
Find the general solution of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5529/Chapter%203_html_m1df5175a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5529/Chapter%203_html_m1df5175a.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5529/Chapter%203_html_m1df5175a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5529/Chapter%203_html_m4d1f7e77.gif)
Therefore, the general solution is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5529/Chapter%203_html_7d218711.gif)
Question 8:
Find the general solution of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_cae8934.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_cae8934.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_cae8934.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_m6e7e7dfe.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_44b71f2a.gif)
Therefore, the general solution is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5530/Chapter%203_html_24f77291.gif)
Question 9:
Find the general solution of the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_39686711.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_39686711.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_39686711.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_m5ac4bcc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_m4ed8b17a.gif)
Therefore, the general solution is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_me194dc2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/163/5531/Chapter%203_html_me194dc2.gif)