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प्रश्न
Find the general solution of : cos x - sin x = 1.
योग
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उत्तर
cos x - sin x = 1
Dividing by `sqrt (1^2 + (-1)) = sqrt2`
`1/sqrt 2 "cos x" - 1/ sqrt 2 "sin x" = 1/ sqrt2`
`"cos" pi/4 "cos x" - "sin" pi/4 "sin x" = 1/ sqrt2`
`"cos" ("x" + pi/4) = "cos" pi/4` ...(i)
The general solution of cos θ = cos α is θ = 2nπ ± `pi/4 ; n ∈ z`
∴ The genera; solution of equation (i) given by
`"x" + pi/4 = 2"n"pi +- pi/4 ; n ∈ z`
`"x" = 2 n pi ; x = 2 n pi - pi/2 ; "n" ∈ z`
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