#### Question

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

#### 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`

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the general solution of : cos x - sin x = 1. Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type.