Question

Heya !!!
Plz solve this step by step.. ​

Answer 1

sin^-1(5/x) + sin^-1(12/x) = π/2

Now,

=>sin^-1(5/x) + sin^-1(12/x) =

sin^-1(12/x) + cos^-1(12/x)

.....(because...cos^-1x + sin^-1x = π/2)

=>sin^-1(5/x) = cos^-1(12/x)

=>sin^-1(5/x) = sin^-1[√{1 - (12/x)^2}]

=>sin^-1(5/x) = sin^-1√{ (x^2 - 144/x^2) }

=> 5/x = √(x^2 - 144)/x

=> 25 = x^2 - 144

=> x^2 = 144 + 25

=> x^2 = 169

=> x = +13 or -13

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Hope it was helpful.