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If sin (sin^-1 (1/5)+ cos^-1 x) = 1, then find the value of x.

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If sin (sin-1 (1/5)+ cos-1 x) = 1, then find the value of x.

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Given, sin (sIn-11/5 + cos-1 x) 1

⇒ sin-1 (1/5) + cos-1 x = sin-11

⇒ sin-1 (1/5) + cos-1(x) = π/2

⇒ sin-1 (1/5) = - cos-1 x

⇒ sin-1 (1/5) = sin-1x

(∵ sin-1x + cos-1x = π/2)

Thus, x = 1/5

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