Check sibling questions

Misc 6 - Prove cos-1 12/13 + sin-1 3/5 = sin-1 56/65 - Miscellaneous

Misc. 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Misc. 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Misc 6 Prove cos-1 12/13 + sin-1 3/5 = sin-1 56/65 Let a = cos-1 12/13 & b = sin-1 3/5 Finding sin a, cos a Let a = cos-1 12/13 cos a = 12/13 We know that sin a = √(1 −cos^2⁡a ) = √(1−(12/13)^2 ) "=" √(25/169) = 5/13 We convert cos-1 to sin-1 & then use sin (a + b) formula Finding sin b, cos b Let b = sin-1 3/5 sin b = 3/5 We know that cos b = √(1 −sin^2⁡b ) =√(1−(3/5)^2 ) "=" √(16/25) "=" 4/5 We know that sin (a + b) = sin a cos b + cos a sin b sin (a + b) = 5/13 × 4/5 + 12/13 × 3/5 = 20/65 + 36/65 = 𝟓𝟔/𝟔𝟓 Putting sin a = 5/13 , cos a = 12/13 & sin b = 3/5 , cos b = 4/5 Thus, sin (a + b) = 56/65 a + b = sin-1 56/65 Putting values cos-1 𝟏𝟐/𝟏𝟑 + sin-1 𝟑/𝟓 = sin-1 𝟓𝟔/𝟔𝟓 Hence L.H.S = R.H.S Hence Proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.