If ⁻¹ ( 5 13 ) + ⁻¹ ( 3 5 ) = ⁻¹(x) , then the value of x is:

Step-by-step solution

Let ⁻¹ ( 5 13 ) = and ⁻¹ ( 3 5 ) = . Then, = 5 13 = 5 12 And, = 3 5 = 4 3 The given equation becomes: ⁻¹ ( 5 12 ) + ⁻¹ ( 4 3 ) = ⁻¹(x) Using the formula ⁻¹A + ⁻¹B = ⁻¹ ( A+B 1-AB ) for AB ⁻¹ ( 5 12 + 4 3 1 - 5 12 4 3 ) = ⁻¹ ( 21 12 16 36 ) = ⁻¹ ( 7 4 9 4 ) = ⁻¹ ( 63 16 ) Let ⁻¹ ( 63 16 ) = = 63 16 . In a right triangle with opposite side 63 and adjacent side 16 , the hypotenuse is 63^2 + 16^2 = 3969 + 256 = 4225 = 65 . Therefore, = Hypotenuse Adjacent = 65 16 . Hence, x = 65 16 . Answer: 65 16