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Exercise 2.1 - Chapter 2 Inverse Trigonometry class 12 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_m34ac5c0c.gif

Answer:

Let sin-1 https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_m76493cdd.gif Then sin y = https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_7f23d2b8.gif

We know that the range of the principal value branch of sin−1 is

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_630b559d.gif and sinhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_m52a394b8.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6152/Chapter%202_html_m10af7c0f.gif

Question 2:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6155/Chapter%202_html_m2199c57.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6155/Chapter%202_html_21c6dd3e.gif

We know that the range of the principal value branch of cos−1 is

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6155/Chapter%202_html_11c3782d.gif.

Therefore, the principal value ofhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6155/Chapter%202_html_44d8e3cb.gif.

Question 3:

Find the principal value of cosec−1 (2)

Answer:

Let cosec−1 (2) = y. Then, https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6157/Chapter%202_html_44bfd2fc.gif

We know that the range of the principal value branch of cosec−1 is https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6157/Chapter%202_html_48c56e9c.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6157/Chapter%202_html_m6570ab7f.gif

Question 4:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6159/Chapter%202_html_m43312614.gif

Answer:

We know that the range of the principal value branch of tan−1 is https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6159/Chapter%202_html_m5dee6bcf.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6159/Chapter%202_html_55e94359.gif

Question 5:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6161/Chapter%202_html_f32d608.gif

Answer:

We know that the range of the principal value branch of cos−1 is

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6161/Chapter%202_html_3c9c7a14.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6161/Chapter%202_html_2729478b.gif

Question 6:

Find the principal value of tan−1 (−1)

Answer:

Let tan−1 (−1) = y. Then, https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6164/Chapter%202_html_m587828a4.gif

We know that the range of the principal value branch of tan−1 is

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6164/Chapter%202_html_m6f71dbaf.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6164/Chapter%202_html_m7edf9658.gif

Question 7:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6169/Chapter%202_html_m36a0c374.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6169/Chapter%202_html_m701b1a3c.gif

We know that the range of the principal value branch of sec−1 is

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6169/Chapter%202_html_m63fd3adb.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6169/Chapter%202_html_490890b8.gif

Question 8:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6173/Chapter%202_html_1e6e5b08.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6173/Chapter%202_html_m61fa0f47.gif

We know that the range of the principal value branch of cot−1 is (0,π) and

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6173/Chapter%202_html_4483fc22.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6173/Chapter%202_html_1fd9c850.gif

Question 9:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6177/Chapter%202_html_3f88ddef.gif

Answer:

We know that the range of the principal value branch of cos−1 is [0,π] and

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6177/Chapter%202_html_1f6e0450.gif.

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6177/Chapter%202_html_5591b560.gif

Question 10:

Find the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6189/Chapter%202_html_m1ceae9b6.gif

Answer:

We know that the range of the principal value branch of cosec−1 is https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6189/Chapter%202_html_384482b9.gif

Therefore, the principal value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6189/Chapter%202_html_m4d1d88dc.gif

Question 11:

Find the value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6194/Item%2011_html_m5f2a02e7.gif

Answer:

Question 12:

Find the value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/6198/Chapter%202_html_6b7da109.gif

Answer:

Question 13:

Find the value of if sin−1 y, then

(A) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_m73e5ee59.gif (B) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_3410905f.gif

(C) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_m39d75a48.gif (D) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_m71e7aca8.gif

Answer:

It is given that sin−1 y.

We know that the range of the principal value branch of sin−1 is https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_1db77eaa.gif

Therefore,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8234/Chapter%202_html_3410905f.gif.

Question 14:

Find the value of https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8235/Chapter%202_html_1a0f6b43.gifis equal to

(A) π (B) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8235/Chapter%202_html_m912018c.gif (C) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8235/Chapter%202_html_m4e8d241e.gif (D) https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/231/8235/Chapter%202_html_552167fc.gif

Answer:

Also Read : Exercise-2.2-Chapter-2-Inverse-Trigonometry-class-12-ncert-solutions-Maths

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