#### Question

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

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#### Solution

cos x − sin x =1

Taking square on both the sides we get,

`therefore (cosx-sinx)^2=1^2`

`thereforecos^2x+sin^2x-2cosxsinx =1`

`therefore 1-2sinxcosx=1`

`therefore 2sinxcosx=0`

`=>sin2x=0`

`=>2x=npi+(-1)^nalpha`

But here α=0

`2x=nπ`

`x=(npi)/2`

The general solution is .

`x=(npi)/2`

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Solution for question: Find the general solution of : cos x - sin x = 1. concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)