What is 1/((sqrt(2))*(sin(x)-cos(x))) ?

The solution to 1/((sqrt(2))*(sin(x)-cos(x))) is 1/(2sin(x-pi/4))

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simplify 1/((sqrt(2))*(sin(x)-cos(x)))

simplify

\frac{1}{( 2 ) \cdot ( sin ( x ) - cos ( x ) )}

\frac{1}{2 sin ( x - \frac{π}{4} )}

Solution steps

\frac{1}{( 2 ) ( sin ( x ) - cos ( x ) )}

Apply rule:

(a) = a

(2) = 2

= \frac{1}{2 ( sin ( x ) - cos ( x ) )}

Simplify

2 (sin (x) - cos (x)) : 2 sin (x - \frac{π}{4})

= \frac{1}{2 sin ( x - \frac{π}{4} )}

(\frac{x - 1}{x})^{2} - (\frac{x + 1}{x})^{2}

3 x^{2} + x^{- 2}

(2 x - 3 x + 6 x^{2} + x) - (x^{5} - 4 x^{2} - x^{2} + 4 x)

\frac{( x + y )}{( x ^{2} - y )} + \frac{( x - 2 y )}{( 3 x ^{2} - 3 y )}

(- 5 a^{3})^{5}

What is 1/((sqrt(2))*(sin(x)-cos(x))) ?
The solution to 1/((sqrt(2))*(sin(x)-cos(x))) is 1/(2sin(x-pi/4))