Sinx - cosx = -sqrt2

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вопрос

To simplify the given expression "sinx - cosx = -sqrt2", we can rewrite it in terms of sine and cosine functions using their identities:

sinx = cos(90° - x)
cosx = cosx

Therefore, sinx - cosx = cos(90° - x) - cosx

Using the angle difference identity for cosine (cos(a - b) = cos a cos b + sin a sin b), we can rewrite the expression:

cos(90° - x) = cos 90° cos x + sin 90° sin x
= 0 cosx + 1 sinx
= sinx

Therefore, sinx - cosx = sinx - cosx = sinx - cosx = -sqrt2

This means that the equation sinx - cosx = -sqrt2 represents the equation sinx - cosx = -sqrt2, which is true.