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If cos (sin^-1 2/5 + cos^-1 x) = 0, then x is equal to

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If cos (sin-1 2/5 + cos-1 x) = 0, then x is equal to

(a) 1/5 (b) 2/5 (c) 0 (d) 1

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(b) 2/5

Given,

cos (sin-1 2/5 + cos-1 x) = 0

So, this can be rewritten as

sin-1 2/5 + cos-1 x = cos-1 0

sin-1 2/5 + cos-1 x = π/2

cos-1 x = π/2 – sin-1 2/5

cos-1 x = cos-1 2/5 [Since, cos-1 x + sin-1 x = π/2]

Hence,

x = 2/5

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