Question

Cos^-1(12/13) =
tan^-1 x , then find x​

Answer 1

Given : Cos⁻¹(12/13) =   tan⁻¹ x  

To Find : x

Solution:

Cos⁻¹(12/13) =   tan⁻¹ x  

Cos⁻¹(12/13) = α

=> 12/13  = Cosα

tan α  =  Sinα  / Cosα

=> tan α  =  (√1 - Cos²α )/ Cosα

=>  tan α  =   (√1 - (12/13)² )/ (12/13)

=>   tan α  =   (√13² - 12² )/12

=>  tan α  =   (√169 - 144 )/12

=>  tan α  =   (√25 )/12

=>  tan α  =   5/12

tan⁻¹ x   = α

=> x =  tan α

=> x = 5/12

x​ = 5/12

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