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Cos A = 0 the general solution is

A = n π + π/2 or n π - π/2 where n is an integer

Cos (x + π/10) = 0

=> x + π/10 = n π + π/2 or n π - π/2

=> x = n π + 2 π/5 or n π - 3 π/5

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Or,

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Cos A = 0 has a general solution of

A = (2 n + 1) π/2 where n an integer (+ve or negative)

hence, Cos (x + π/10) = 0 has the solution of

x + π/10 = (2 n + 1) π/2

x = n π + 2π/5 where n is an integer.

A = n π + π/2 or n π - π/2 where n is an integer

Cos (x + π/10) = 0

=> x + π/10 = n π + π/2 or n π - π/2

=> x = n π + 2 π/5 or n π - 3 π/5

===============

Or,

========

Cos A = 0 has a general solution of

A = (2 n + 1) π/2 where n an integer (+ve or negative)

hence, Cos (x + π/10) = 0 has the solution of

x + π/10 = (2 n + 1) π/2

x = n π + 2π/5 where n is an integer.