# Chapter - TRIGONOMETRY Std- 10 sub- mathematics QUESTION: if cos(x) + sin(x) = sqrt2 cos(x) , then prove that cos(x) - sin(x) = sqrt2 sin(x)

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### 1 Answer

You need to write sin x in terms of cos x, using the condition provided by the problem, such that:

`sin x = sqrt2*cos x - cos x`

You need to substitute `sqrt2*cos x - cos x` for sin x in the identity to be proved such that:

`cos x - (sqrt2*cos x - cos x) = sqrt2 sin x`

You need to open the brackets such that:

`cos x - sqrt2*cos x + cos x = sqrt2*sin x`

`cos x - sqrt2*cos x = sqrt2*sin x`

You need to factor out cos x such that:

`cos x(1 - sqrt2) = sqrt2*sin x`

**Notice that the left side is not equal to the right side, hence, the expression `cos(x) - sin(x) = sqrt2 sin(x)` is not an identity.**

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