Question

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

Answer 1

Given :

• sin( x ) + a cos( x ) = b

To Find :

• | a sin( x ) - cos( x ) | = ?

Solution :

$\dashrightarrow \: \: \tt \sin(x) + a \cos(x) = b$

• Differentiate with respect to x

$\dashrightarrow \: \: \tt \: \frac{d}{dx} \bigg( \sin(x) + a \cos(x) \bigg) = \frac{d}{dx} (b)$

$\dashrightarrow \: \tt \: \cos(x) - a \sin(x) = 0$

${ { \dashrightarrow }}\tt \: \: \bigg(a \sin(x) - \cos(x) \bigg) = 0$

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

$\\ \\ \dashrightarrow \: \: { \underline{\boxed{ \mathfrak{ |a \sin(x) - \cos(x) | = 0}}}}$