Chapter 2 Class 12 Inverse Trigonometric Functions
Ex 2.1, 8 Important
Ex 2.1, 12 Important
Ex 2.1, 14 (MCQ) Important
Example 4 Important
Question 3 Deleted for CBSE Board 2024 Exams
Question 4 Important Deleted for CBSE Board 2024 Exams
Question 6 Important Deleted for CBSE Board 2024 Exams
Ex 2.2, 13 (MCQ) Important
Ex 2.2, 15 (MCQ)
Question 4 Important Deleted for CBSE Board 2024 Exams
Question 6 Important Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Misc 2 Important
Misc 7 Important You are here
Misc 9 Important
Misc 10 Important
Question 2 Important Deleted for CBSE Board 2024 Exams
Question 3 (MCQ) Deleted for CBSE Board 2024 Exams
Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at April 16, 2024 by Teachoo
Misc 7 Prove tan–1 63/16 = sin–1 5/13 + cos–1 3/5 Let a = sin–1 5/13 , b = cos–1 3/5 Finding tan a & tan b We convert sin–1 & cos–1 to tan–1 & then use tan (a + b) formula Let a = sin–1 𝟓/𝟏𝟑 sin a = 5/13 We know that cos a = √(1 –sin2 𝑎) = √("1 – " (5/13)^2 ) = √(144/169) = 12/13 Now, tan a = (sin 𝑎)/(cos a) = (5/13)/(12/13) = 5/13×13/12 = 5/12 Let b = cos–1 𝟑/𝟓 cos b = 3/5 We know that sin b = √("1 – cos2 b" ) = √("1 –" (3/5)^2 ) =√(16/25) = 4/5 Now, tan b = sin𝑏/cos𝑏 = (4/5)/(3/5) = 4/5×5/3 = 4/3 Now we know that tan (a + b) = 𝑡𝑎𝑛〖𝑎 +〖 𝑡𝑎𝑛〗〖𝑏 〗 〗/(1 − 𝑡𝑎𝑛〖𝑎 𝑡𝑎𝑛𝑏 〗 ) Putting tan a = 5/12 & tan b = 4/3 tan (a + b) = (5/12 + 4/3)/(1 − 5/12 × 4/3) = ((5 × 3 + 4 × 12)/36)/(1 − 20/36) = ((15 + 48)/36)/((36 − 20)/36) = (63/36)/(16/36) = 63/36×36/16 = 𝟔𝟑/𝟏𝟔 Thus, tan (a + b) = 63/16 a + b = tan–1 (63/16) Putting values of a & b sin-1 𝟓/𝟏𝟑 + cos–1 𝟑/𝟓 = tan–1 (𝟔𝟑/𝟏𝟔) Hence L.H.S = R.H.S Hence Proved