Question

Question 7: Prove tan¯¹ 63/16 = sin¯¹ 5/13 + cos¯¹ 3/5

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

cos^2a=1-sin^2aormula use .

a=sin^-1 5/13. same do apply formula u get

Answer 2

 To prove :

⇒ tan¯¹ 63/16 = sin¯¹ 5/13 + cos¯¹ 3/5
 
Taking R.H.S. :

⇒ sin¯¹ 5/13 + cos¯¹ 3/5
⇒ tan¯¹ 5/12 + tan¯¹ 4/3
⇒ tan¯¹ [ ( 5/12 + 4/3 ) / ( 1 - 5/12 ×4/3 ) ]
⇒ tan¯¹ [ { (15 + 48)/36 } / { (36 - 20) / 36 } ]
⇒ tan¯¹ (63 / 13)

Hope it helps!!!