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Sum

Find the general solution of : cos x - sin x = 1.

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#### Solution

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`

Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type

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