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  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise

Transcript

Ex 2.1, 12 Find the value of cosโˆ’1 (1/2) + 2 sinโˆ’1 (1/2) Solving cosโˆ’1 (๐Ÿ/๐Ÿ) Let y = cosโˆ’1 (1/2) cos y = (1/2) cos y = cos (ฯ€/3) Range of principal value of cosโˆ’1 is [0 , ๐œ‹] Hence, the principal value is ฯ€/3. Rough We know that cos 60ยฐ = 1/2 ฮธ = 60ยฐ = 60ยฐ ร— ๐œ‹/180 = ๐œ‹/3 Since 1/2 is positive Principal value is ฮธ i.e. ๐œ‹/3 Solving sinโˆ’1 (๐Ÿ/๐Ÿ) Let y = sinโˆ’1 (1/2) sin y = 1/2 sin y = sin (ฯ€/6) Range of principal value of sinโˆ’1 is [(โˆ’๐œ‹)/2 " , " ๐œ‹/2] Hence, the principal value is ฯ€/6 Rough We know that sin 30ยฐ = 1/2 ฮธ = 30ยฐ = 30 ร— ๐œ‹/180 = ๐œ‹/6 Since 1/2 is positive Principal value is ฮธ i.e. ๐œ‹/6 Now we have cosโˆ’1 1/2 = ๐œ‹/3 & sinโˆ’1 1/2 = ๐œ‹/6 Solving cosโˆ’1 ๐Ÿ/๐Ÿ + 2sinโˆ’1 ๐Ÿ/๐Ÿ = ๐œ‹/3 + 2 ร— ๐œ‹/6 = ๐œ‹/3 + ๐œ‹/3 = (๐œ‹ + ๐œ‹)/3 = ๐Ÿ๐…/๐Ÿ‘

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.