.If sin x+a cos x=b, then what is the expression for |a sin x-cos x| in terms of a and b?

1 thought on “.If sin x+a cos x=b, then what is the expression for |a sin x-cos x| in terms of a and b?”

1. Given :

   • sin( x ) + a cos( x ) = b

   To Find :

   • | a sin( x ) – cos( x ) | = ?

   Solution :

   [tex] \dashrightarrow \: \: \tt \sin(x) + a \cos(x) = b \\ \\ [/tex]

   • Differentiate with respect to x

   [tex] \dashrightarrow \: \: \tt \: \frac{d}{dx} \bigg( \sin(x) + a \cos(x) \bigg) = \frac{d}{dx} (b) \\ \\ [/tex]

   [tex] \dashrightarrow \: \tt \: \cos(x) – a \sin(x) = 0 \\ \\ [/tex]

   [tex]{ { \dashrightarrow }}\tt \: \: \bigg(a \sin(x) – \cos(x) \bigg) = 0 \\ \\ [/tex]

   • From this expression we can say, this function is always 0 for all real values of x

   [tex]\\ \\ \dashrightarrow \: \: { \underline{\boxed{ \mathfrak{ |a \sin(x) – \cos(x) | = 0}}}} \\ \\ [/tex]

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