What is sin(x-pi/4)-1 ?

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

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simplify sin(x-pi/4)-1

simplify

sin (x - \frac{π}{4}) - 1

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

Solution steps

sin (x - \frac{π}{4}) - 1

Rewrite using trig identities

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

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

= sin (x - \frac{π}{4}) - 1

Use the Angle Difference identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

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

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

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

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

\frac{1}{cot ( θ ) sin ( - θ )}

- 3 (\frac{3 sin ( - nπ )}{πn})

3 cos (x - \frac{π}{3})

a sin (- \frac{4}{3})

sin (arccos (7 x))

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